Graphic summary
  • Show / hide key
  • Information


Scientific and technological production
  •  

1 to 50 of 114 results
  • Access to the full text
    Spectral properties of the connectivity matrix and the SIS-epidemic threshold for mid-size metapopulations  Open access

     Juher Barrot, David; Mañosa Fernández, Víctor
    Mathematical modeling of natural phenomena
    Vol. 9, num. 2, p. 108-120
    DOI: 10.1051/mmnp/20149207
    Date of publication: 2014-04-24
    Journal article

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    We consider the spread of an infectious disease on a heterogeneous metapopulation defined by any (correlated or uncorrelated) network. The infection evolves under transmission, recovery and migration mechanisms. We study some spectral properties of a connectivity matrix arising from the continuous-time equations of the model. In particular we show that the classical sufficient condition of instability for the disease-free equilibrium, well known for the particular case of uncorrelated networks, works also for the general case. We give also an alternative condition that yields a more accurate estimation of the epidemic threshold for correlated (either assortative or dissortative) networks.

    We consider the spread of an infectious disease on a heterogeneous metapopulation defined by any (correlated or uncorrelated) network. The infection evolves under transmission, recovery and migration mechanisms. We study some spectral properties of a connectivity matrix arising from the continuous-time equations of the model. In particular we show that the classical sufficient condition of instability for the disease-free equilibrium, well known for the particular case of uncorrelated networks, works also for the general case. We give also an alternative condition that yields a more accurate estimation of the epidemic threshold for correlated (either assortative or dissortative) networks.

    Postprint (author’s final draft)

  • Basin of attraction of triangular maps with applications

     Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor
    Journal of difference equations and applications
    Vol. 20, num. 3, p. 423-437
    DOI: 10.1080/10236198.2013.852187
    Date of publication: 2014-03
    Journal article

    Read the abstract Read the abstract View View Open in new window  Share Reference managers Reference managers Open in new window

    We consider planar triangular maps that preserve certain fibration of the plane. We assume that there exists an invariant attracting fiber and we study the limit dynamics of those points in the basin of attraction of this invariant fiber, assuming that either it contains a global attractor, or it is filled by fixed or 2-periodic points. We apply our results to several examples.

    We consider planar triangular maps that preserve certain fibration of the plane. We assume that there exists an invariant attracting fiber and we study the limit dynamics of those points in the basin of attraction of this invariant fiber, assuming that either it contains a global attractor, or it is filled by fixed or 2-periodic points. We apply our results to several examples.

    Postprint (author’s final draft)

  • Access to the full text
    Periodic orbits of planar integrable birational maps  Open access

     Gálvez Carrillo, Maria Immaculada; Mañosa Fernández, Víctor
    Date: 2014-02-14
    Report

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    A birational planar map F possessing a rational first integral preserves a foliation of the plane given by algebraic curves which, if F is not globally periodic, is given by a foliation of curves that have generically genus 0 or 1. In the genus 1 case, the group structure of the foliation characterizes the dynamics of any birational map preserving it. We will see how to take advantage of this structure to find periodic orbits of such maps.

    A birational planar map F possessing a rational first integral preserves a foliation of the plane given by algebraic curves which, if F is not globally periodic, is given by a foliation of curves that have generically genus 0 or 1. In the genus 1 case, the group structure of the foliation characterizes the dynamics of any birational map preserving it. We will see how to take advantage of this structure to find periodic orbits of such maps.

  • Access to the full text
    Dynamics of integrable birational maps preserving genus 0 foliations  Open access

     Llorens, Mireia; Mañosa Fernández, Víctor
    Date: 2014-10-03
    Report

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    Pòster presentat al congrés NPDDS2014

  • Dynamics of integrable birational maps preserving genus 0 foliations

     Llorens, Mireia; Mañosa Fernández, Víctor
    New Perspectives in Discrete Dynamical Systems
    p. 40
    Presentation's date: 2014-10-03
    Presentation of work at congresses

     Share Reference managers Reference managers Open in new window

  • Access to the full text
    Integrability and non-integrability of periodic non-autonomous Lyness recurrences  Open access

     Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor
    Dynamical systems: an international journal
    Vol. 28, num. 4, p. 518-538
    DOI: 10.1080/14689367.2013.821103
    Date of publication: 2013-12-01
    Journal article

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    This paper studies non-autonomous Lyness-type recurrences of the form x_{n+2} = (a_n + x_{n+1})/x n , where a_n is a k-periodic sequence of positive numbers with primitive period k. We show that for the cases k in {1, 2, 3, 6}, the behaviour of the sequence x_n is simple (integrable), while for the remaining cases satisfying this behaviour can be much more complicated (chaotic). We also show that the cases where k is a multiple of 5 present some different features.

    This paper studies non-autonomous Lyness-type recurrences of the form x n+2 = (a n + x n+1)/x n , where {a n } is a k-periodic sequence of positive numbers with primitive period k. We show that for the cases k {1, 2, 3, 6}, the behaviour of the sequence {x n } is simple (integrable), while for the remaining cases satisfying this behaviour can be much more complicated (chaotic). We also show that the cases where k is a multiple of 5 present some different features.

  • Access to the full text
    Global periodicity conditions for maps and recurrences via normal forms  Open access

     Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor
    International journal of bifurcation and chaos
    Vol. 23, num. 11, p. 1350182-1-1350182-18
    DOI: 10.1142/S0218127413501824
    Date of publication: 2013-11
    Journal article

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    We face the problem of characterizing the periodic cases in parametric families of rational diffeomorphisms of ¿^k, where ¿ is R or C, having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the existence of a formal linearization of the map, and on the introduction of a suitable rational parametrization of the parameters of the family. Using these tools we can find a finite set of values p for which the map can be p-periodic, reducing the problem of finding the parameters for which the periodic cases appear to simple computations. We apply our results to several two- and three-dimensional classes of polynomial or rational maps. In particular, we find the global periodic cases for several Lyness-type recurrences.

    We face the problem of characterizing the periodic cases in parametric families of rational diffeomorphisms of K, where K is ℝ or ℂ, having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the existence of a formal linearization of the map, and on the introduction of a suitable rational parametrization of the parameters of the family. Using these tools we can find a finite set of values p for which the map can be p-periodic, reducing the problem of finding the parameters for which the periodic cases appear to simple computations. We apply our results to several two- and three-dimensional classes of polynomial or rational maps. In particular, we find the global periodic cases for several Lyness-type recurrences.

    Postprint (author’s final draft)

  • Access to the full text
    On the set of periods of the 2-periodic Lyness¿ Equation  Open access

     Bastien, Guy; Mañosa Fernández, Víctor; Rogalski, Marc
    Date: 2013-07-25
    Report

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    We study the periodic solutions of the non--autonomous periodic Lyness' recurrence u_{n+2}=(a_n+u_{n+1})/{u_n}, where a_n is a cycle with positive values a,b and with positive initial conditions. Among other methodological issues we give an outline of the proof of the following results: (1) If (a,b)\neq(1,1), then there exists a value p_0(a,b) such that for any p>p_0(a,b) there exist continua of initial conditions giving rise to 2p--periodic sequences. (2) The set of minimal periods arising when a and b are positive and positive initial conditions are considered, contains all the even numbers except 4, 6, 8, 12 and 20. If a\neq b, then it does not appear any odd period, except 1.

    We study the periodic solutions of the non–autonomous periodic Lyness’ recurrence un+2 = (an +un+1)=un, where fangn is a cycle with positive values a,b and with positive initial conditions. Among other methodological issues we give an outline of the proof of the following results: (1) If (a;b) 6= (1;1), then there exists a value p0(a;b) such that for any p > p0(a;b) there exist continua of initial conditions giving rise to 2p–periodic sequences. (2) The set of minimal periods arising when (a;b) 2 (0;¥) 2 and positive initial conditions are considered, contains all the even numbers except 4, 6, 8, 12 and 20. If a 6= b, then it does not appear any odd period, except 1.

  • Access to the full text
    Different approaches to the global periodicity problem  Open access

     Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor; Mañosas, Francesc
    Date: 2013-07-25
    Report

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    Let F be a real or complex n-dimensional map. It is said that F is globally periodic if there exists some p such that F^p(x)=x for all x. The minimal p satisfying this property is called the period of F. Given a m-dimensional parametric family of maps, say F_\lambda, a problem of current interest is to determine all the values of \lambda such that F_\lambda is globally periodic, together with their corresponding periods. The aim of this paper is to show some techniques that we use to face this question, as well as some recent results that we have obtained. We will focus on proving the equivalence of the problem with the complete integrability of the dynamical system induced by the map F, and related issues; on the use of the local linearization given by the Bochner Theorem; and on the use the Normal Form theory. We also present some open questions in this setting.

    t Let F be a real or complex n-dimensional map. It is said that F is globally periodic if there exists some p ∈ N + such that Fp(x) = x for all x, where F k = F ◦ F k−1, k ≥ 2. The minimal p satisfying this property is called the period of F. Given a m-dimensional parametric family of maps, say Fλ, a problem of current interest is to determine all the values of λ such that Fλ is globally periodic, together with their corresponding periods. The aim of this paper is to show some techniques that we use to face this question, as well as some recent results that we have obtained. We will focus on proving the equivalence of the problem with the complete integrability of the dynamical system induced by the map F, and related issues; on the use of the local linearization given by the Bochner Theorem; and on the use the Normal Form theory. We also present some open questions in this setting.

  • Access to the full text
    Periodic orbits of planar integrable birational maps  Open access

     Mañosa Fernández, Víctor
    Date: 2013-09-03
    Report

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    A birational planar map F possessing a rational first integral, preserves a foliation of the plane given by algebraic curves which, in the case that F is not globally periodic, generically is given by a foliation of conics or elliptic curves. In the latter case, the group structure of the elliptic foliation characterizes the dynamics of any birational map preserving it. We will see how to take advantage of this structure for searching periodic orbits of such maps.

    Conferència convidada al congrés NOMA'13.

  • Access to the full text
    Basin of attraction of triangular maps with applications  Open access

     Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor
    Date: 2013-07-25
    Report

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    We consider some planar triangular maps. These maps preserve certain fibration of the plane. We assume that there exists an invariant attracting fiber and we study the limit dynamics of those points in the basin of attraction of this invariant fiber, assuming that either it contains a global attractor, or it is filled by fixed or $2$-periodic points. Finally, we apply our results to a variety of examples, from particular cases of triangular systems to some planar quasi-homogeneous maps, and some multiplicative and additive difference equations, as well.

    We consider some planar triangular maps. These maps preserve certain fibration of the plane. We assume that there exists an invariant attracting fiber and we study the limit dynamics of those points in the basin of attraction of this invariant fiber, assuming that either it contains a global attractor, or it is filled by fixed or 2-periodic points. Finally, we apply our results to a variety of examples, from particular cases of triangular systems to some planar quasi-homogeneous maps, and some multiplicative and additive difference equations, as well.

  • Access to the full text
    Spectral properties of the connectivity matrix and the SIS-epidemic threshold for mid-size metapopulations  Open access

     Juher Barrot, David; Mañosa Fernández, Víctor
    Date: 2013-05-10
    Report

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    We consider the spread of an infectious disease on a heterogeneous metapopulation defined by any (correlated or uncorrelated) network. The infection evolves under transmission, recovering and migration mechanisms. We study some spectral properties of a connectivity matrix arising from the continuous-time equations of the model. In particular we show that the classical sufficient condition of instability for the disease-free equilibrium, well known for the particular case of uncorrelated networks, works also for the general case. We give also an alternative condition that yields a more accurate estimation of the epidemic threshold for correlated (either assortative or dissortative) networks.

    We consider the spread of an infectious disease on a heterogeneous metapopulation defined by any (correlated or uncorrelated) network. The infection evolves under transmission, recovering and migration mechanisms. We study some spectral properties of a connectivity matrix arising from the continuous-time equations of the model. In particular we show that the classical sufficient condition of instability for the disease-free equilibrium, well known for the particular case of uncorrelated networks, works also for the general case. We give also an alternative condition that yields a more accurate estimation of the epidemic threshold for correlated (either assortative or dissortative) networks

  • Access to the full text
    On periodic solutions of 2-periodic Lyness' equations  Open access

     Bastien, Guy; Mañosa Fernández, Víctor; Rogalski, Marc
    International journal of bifurcation and chaos
    Vol. 23, num. 4, p. 1350071-1-1350071-18
    DOI: 10.1142/S0218127413500715
    Date of publication: 2013-04
    Journal article

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    We study the existence of periodic solutions of the non--autonomous periodic Lyness' recurrence u_{n+2}=(a_n+u_{n+1})/u_n, where {a_n}_n is a cycle with positive values a,b and with positive initial conditions. It is known that for a=b=1 all the sequences generated by this recurrence are 5-periodic. We prove that for each pair (a,b) is not (1,1) there are infinitely many initial conditions giving rise to periodic sequences, and that the family of recurrences have almost all the even periods. If a is different from b, then any odd period, except 1, appears.

    We study the existence of periodic solutions of the nonautonomous periodic Lyness' recurrenceun+2 = (an + un+1)/un, where {an}n is a cycle with positive values a, b and with positive initial conditions. It is known that for a = b = 1 all the sequences generated by this recurrence are 5-periodic. We prove that for each pair (a, b) ≠ (1, 1) there are infinitely many initial conditions giving rise to periodic sequences, and that the family of recurrences have almost all the even periods. If a ≠ b, then any odd period, except 1, appears.

    Postprint (author’s final draft)

  • Periodic orbits of planar integrable birational maps

     Mañosa Fernández, Víctor
    International Workshop on Nonlinear Maps and their Applications
    p. 4
    Presentation's date: 2013-09-03
    Presentation of work at congresses

    Read the abstract Read the abstract View View Open in new window  Share Reference managers Reference managers Open in new window

    A birational planar map F possessing a rational first integral, preserves a foliation of the plane given by algebraic curves which, in the case that F is not globally periodic, generically is given by a foliation of conics or elliptic curves. In the latter case, the group structure of the elliptic foliation characterizes the dynamics of any birational map preserving it. We will see how to take advantage of this structure for searching periodic orbits of such maps.

  • Access to the full text
    Integrability and non-integrability of periodic non-autonomous Lyness recurrences (revised and enlarged version)  Open access

     Cima, Anna; Gasull, Armengol; Mañosa Fernández, Víctor
    Date: 2012-12-22
    Report

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    This paper studies non-autonomous Lyness type recurrences of the form xn+2 = (an+xn+1)=xn, where fang is a k-periodic sequence of positive numbers with primitive period k. We show that for the cases k 2 f1; 2; 3; 6g the behavior of the sequence fxng is simple (integrable) while for the remaining cases satisfying this behavior can be much more complicated (chaotic). We also show that the cases where k is a multiple of 5 present some di erent features.

    Preprint. Versió revisada i augmentada d'un anterior report homònim.

  • Access to the full text
    Global periodicity conditions for maps and recurrences via Normal Forms  Open access

     Cima, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor
    Date: 2012-05-04
    Report

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    We face the problem of characterizing the periodic cases in parametric families of (real or complex) rational diffeomorphisms having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the existence of a formal linearization of the map, and on the introduction of a suitable rational parametrization of the parameters of the family. Using these tools we can find a finite set of values p for which the map can be p-periodic, reducing the problem of finding the parameters for which the periodic cases appear to simple computations. We apply our results to several two and three dimensional classes of polynomial or rational maps. In particular we find the global periodic cases for several Lyness type recurrences

  • Access to the full text
    A presentation on periodic solutions of 2-periodic Lyness difference equations  Open access

     Bastien, Guy; Mañosa Fernández, Víctor; Rogalski, Marc
    Date: 2012-07-27
    Report

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    PDF amb el contingut de la presentació al 18th ICDEA de Barcelona

  • Access to the full text
    Periodic orbits of integrable birational maps on the plane: blending dynamics and algebraic geometry, the Lyness' case  Open access

     Bastien, Guy; Mañosa Fernández, Víctor; Rogalski, Marc
    Date: 2012-10
    Report

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    Contingut del Pòster presentat al congrés New Trends in Dynamical Systems

  • Access to the full text
    On periodic solutions of 2-periodic Lyness difference equations  Open access

     Bastien, Guy; Mañosa Fernández, Víctor; Rogalski, Marc
    Date: 2012-01-04
    Report

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    We study the existence of periodic solutions of the non--autonomous periodic Lyness' recurrence u_{n+2}=(a_n+u_{n+1})/u_n, where {a_n} is a cycle with positive values a,b and with positive initial conditions. It is known that for a=b=1 all the sequences generated by this recurrence are 5-periodic. We prove that for each pair (a,b) different from (1,1) there are infinitely many initial conditions giving rise to periodic sequences, and that the family of recurrences have almost all the even periods. If a is not equal to b, then any odd period, except 1, appears.

  • Análisis e identificación de sistemas con histéresis usando órbitas periódicas

     Pujol Vazquez, Gisela; Mañosa Fernández, Víctor; Giri, F.; Fuad, Mohammad; Ikhouane, Fayçal
    Competitive project

     Share

  • Rational periodic sequences for the Lyness recurrence

     Gasull, Armengol; Mañosa Fernández, Víctor; Xarles Ribas, Xavier
    Discrete and continuous dynamical systems. Series A
    Vol. 32, num. 2, p. 587-604
    DOI: 10.3934/dcds.2012.32.587
    Date of publication: 2012-02-01
    Journal article

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • Access to the full text
    On 2- and 3-periodic Lyness difference equations  Open access

     Cima, Anna; Gasull, Armengol; Mañosa Fernández, Víctor
    Journal of difference equations and applications
    Vol. 18, num. 5, p. 849-864
    DOI: 10.1080/10236198.2010.524212
    Date of publication: 2012-05-11
    Journal article

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    We describe the sequences {xn}n given by the non-autonomous second-order Lyness difference equations xnþ2 ¼ ðan þ xnþ1Þ=xn, where {an}n is either a 2-periodic or a 3- periodic sequence of positive values and the initial conditions x1; x2 are also positive. We also show an interesting phenomenon of the discrete dynamical systems associated with some of these difference equations: the existence of one oscillation of their associated rotation number functions. This behaviour does not appear for the autonomous Lyness difference equations

    Postprint (author’s final draft)

    This is an electronic version of an article published in "Anna Cima, Armengol Gasull & Vííctor Maññosa (2011): On 2- and 3- periodic Lyness difference equations, Journal of Difference Equations and Applications,2012, 18,5,849-864 DOI:10.1080/10236198.2010.524212"

  • Access to the full text
    Non-autonomous two periodic Gumovski-Mira difference equations  Open access

     Cima, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor
    International journal of bifurcation and chaos
    Vol. 22, num. 11, p. 1250264-1-1250264-14
    DOI: 10.1142/S0218127412502641
    Date of publication: 2012-12
    Journal article

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    We consider two types of nonautonomous two-periodic Gumovski–Mira difference equations. We show that while the corresponding autonomous recurrences are conjugated, the behavior of the sequences generated by the two-periodic ones differ dramatically: in one case the behavior of the sequences is simple (integrable) and in the other case it is much more complicated (chaotic). We also present a global study of the integrable case that includes which periods appear for the recurrence.

    Postprint (author’s final draft)

  • Periodic orbits of integrable birational maps on the plane: blending dynamics and algebraic geometry, the Lyness' case

     Mañosa Fernández, Víctor
    New Trends in Dynamical Systems
    p. 55-56
    Presentation's date: 2012-10-04
    Presentation of work at congresses

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • On periodic solutions of 2-periodic Lyness difference equations

     Bastien, Guy; Mañosa Fernández, Víctor; Rogalski, Marc
    International Conference on Difference Equations and Applications
    p. 49
    Presentation's date: 2012-07-27
    Presentation of work at congresses

     Share Reference managers Reference managers Open in new window

  • Access to the full text
    Non autonomous 2-periodic Gumovski-Mira difference equations  Open access

     Cima, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor
    Date: 2011-06-01
    Report

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    We consider two types of non-autonomous 2-periodic Gumovski-Mira difference equations. We show that while the corresponding autonomous recurrences are conjugated, the behavior of the sequences generated by the 2-periodic ones di er dramatically: in one case the behavior of the sequences is simple (integrable) and in the other case it is much more complicated (chaotic). We also present a global study of the integrable case that includes which periods appear for the recurrence.

  • Access to the full text
    Decentralized H-infinity control of systems with information structure constraints  Open access

     Rossell Garriga, Josep Maria; Palacios Quiñonero, Francisco; Luo Ren, Ningsu; Mañosa Fernández, Víctor
    Workshop on Control Dynamics, Monitoring and Applications
    p. 57-62
    Presentation's date: 2011-02-07
    Presentation of work at congresses

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    The paper deals with a class of continuous-time statedelayed uncertain systems considering H-infinity control. The main objective is to design static output feedback controllers satisfying three requirements simultaneously: asymptotic stability for the closed-loop system, a minimum effect of the disturbance input on the controlled output, and the obtention of a gain matrix having an arbitrarily preassigned zerononzero structure. To solve this problem, a linear matrix inequality (LMI) delay-independent approach is derived. A numerical example illustrates the effectiveness of the proposed method

  • Access to the full text
    Integrability and non-integrability of periodic non-autonomous Lyness recurrences  Open access

     Cima, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor
    Date: 2010-12-22
    Report

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    This paper studies non-autonomous Lyness type recurrences of the form x_{n+2}=(a_n+x_n)/x_{n+1}, where a_n is a k-periodic sequence of positive numbers with prime period k. We show that for the cases k in {1,2,3,6} the behavior of the sequence x_n is simple(integrable) while for the remaining cases satisfying k not a multiple of 5 this behavior can be much more complicated(chaotic). The cases k multiple of 5 are studied separately.

  • Dinámica, Atractores y Nolinealidad: Caos y Estabilidad

     Mañosa Fernández, Víctor; Jorba ., Angel
    Competitive project

     Share

  • Access to the full text
    Rational periodic sequences for the Lyness recurrence  Open access

     Gasull Embid, Armengol; Mañosa Fernández, Víctor; Xarles Ribas, Xavier
    Date: 2010-04-30
    Report

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    Consider the celebrated Lyness recurrence $x_{n+2}=(a+x_{n+1})/x_{n}$ with $a\in\Q$. First we prove that there exist initial conditions and values of $a$ for which it generates periodic sequences of rational numbers with prime periods $1,2,3,5,6,7,8,9,10$ or $12$ and that these are the only periods that rational sequences $\{x_n\}_n$ can have. It is known that if we restrict our attention to positive rational values of $a$ and positive rational initial conditions the only possible periods are $1,5$ and $9$. Moreover 1-periodic and 5-periodic sequences are easily obtained. We prove that for infinitely many positive values of $a,$ positive 9-period rational sequences occur. This last result is our main contribution and answers an open question left in previous works of Bastien \& Rogalski and Zeeman. We also prove that the level sets of the invariant associated to the Lyness map is a two-parameter family of elliptic curves that is a universal family of the elliptic curves with a point of order $n, n\ge5,$ including $n$ infinity. This fact implies that the Lyness map is a universal normal form for most birrational maps on elliptic curves.

  • Access to the full text
    On Poncelet's maps  Open access

     Cima, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor
    Computers & mathematics with applications
    Vol. 60, num. 5, p. 1457-1464
    DOI: 10.1016/j.camwa.2010.06.027
    Date of publication: 2010-08-08
    Journal article

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    Given two ellipses, one surrounding the other one, Poncelet introduced a map P from the exterior one to itself by using the tangent lines to the interior ellipse. This procedure can be extended to any two smooth, nested and convex ovals and we call this type of maps, Poncelet’s maps. We recall what he proved around 1814 in the dynamical systems language: In the two ellipses case and when the rotation number of P is rational there exists a n ∈ N such that Pn = Id, or in other words, the Poncelet’s map is conjugate to a rational rotation. In this paper we study general Poncelet’s maps and give several examples of algebraic ovals where the corresponding Poncelet’s map has a rational rotation number and it is not conjugate to a rotation. Finally, we also provide a new proof of Poncelet’s result based on dynamical and computational tools.

    Postprint (author’s final draft)

  • Access to the full text
    On two and three periodic Lyness difference equations  Open access

     Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor
    Date: 2009-12-26
    Report

    Read the abstract Read the abstract Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

    We describe the sequences {x_n}_n given by the non-autonomous second order Lyness difference equations x_{n+2}=(a_n+x_{n+1})/x_n, where {a_n}_n is either a 2-periodic or a 3-periodic sequence of positive values and the initial conditions x_1,x_2 are as well positive. We also show an interesting phenomenon of the discrete dynamical systems associated to some of these difference equations: the existence of one oscillation of their associated rotation number functions. This behavior does not appear for the autonomous Lyness difference equations.

  • CONTROL, DINÀMICA I APLICACIONS (CODALAB)

     Ikhouane, Fayçal; Gharibnezhad, Fahit; Galvis Restrepo, Eduard; Acho Zuppa, Leonardo; Tibaduiza Burgos, Diego Alexander; Mantecon Baena, Juan Antonio; Mujica Delgado, Luis Eduardo; Mañosa Fernández, Víctor; Palacios Quiñonero, Francisco; Pozo Montero, Francesc; Pujol Vazquez, Gisela; Rossell Garriga, Josep Maria; Vidal Segui, Yolanda; Rubió Massegú, Josep; Ismail Abdelkareem Moustafa, Mohammed; Rodellar Benede, Jose Julian
    Competitive project

     Share

  • CONTROL DESCENTRALIZADO DE SISTEMAS EN RED A GRAN ESCALA CON INCERTIDUMBRES Y RETARDOS

     Palacios Quiñonero, Francisco; Mañosa Fernández, Víctor; Rossell Garriga, Josep Maria
    Competitive project

     Share

  • On Poncelet-type maps.

     Mañosa Fernández, Víctor
    International Conference on Difference Equations and Applications
    p. 69
    Presentation's date: 2009-10-22
    Presentation of work at congresses

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • Access to the full text
    Identification of one-parameter bifurcations giving rise to periodic orbits, from their period function  Open access

     Gasull Embid, Armengol; Mañosa Fernández, Víctor; Villadelprat Yagüe, Jordi
    International Workshop on Dynamics and Control
    Presentation's date: 2009-06-01
    Presentation of work at congresses

    Access to the full text Access to the full text Open in new window  Share Reference managers Reference managers Open in new window

  • Control descentralizado de sistemas en red a gran escala con incertidumbres y retardos (proyecto coordinado)

     Mañosa Fernández, Víctor; Rossell Garriga, Josep Maria
    Competitive project

     Share

  • Global dynamics of discrete systems through Lie Symmetries.

     Mañosa Fernández, Víctor
    Mathematical models in engeneering, biology and medecine. Conference on boundary value problems.
    Presentation's date: 2008-09-01
    Presentation of work at congresses

     Share Reference managers Reference managers Open in new window

  • Estudio de sistemas dinámicos discretos vía ecuaciones diferenciales

     Mañosa Fernández, Víctor
    NoLineal 2008
    Presentation's date: 2008-06-16
    Presentation of work at congresses

     Share Reference managers Reference managers Open in new window

  • On Poncelet's maps

     Cima, A; Mañosa Fernández, Víctor; Gasull, A
    Date: 2008-12
    Report

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • Studying discrete dynamical systems through differential equations

     Cima, A; Gasull, A; Mañosa Fernández, Víctor
    Journal of differential equations
    Vol. 224, num. 3, p. 630-648
    Date of publication: 2008-02
    Journal article

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • A note on globally periodic maps and integrability

     Mañosa Fernández, Víctor
    Journal of difference equations and applications
    Vol. 14, num. 6, p. 667-670
    Date of publication: 2008-06
    Journal article

     Share Reference managers Reference managers Open in new window

  • Some properties of the k-dimensional Lyness' map

     Cima, A; Gasull, A; Mañosa Fernández, Víctor
    Journal of physics A. Mathematical and theoretical
    Vol. 41, p. 85205-85223
    Date of publication: 2008-06
    Journal article

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • Dynamic properties of the hysteretic Bouc-Wen model

     Ikhouane, Fayçal; Mañosa Fernández, Víctor; Rodellar Benede, Jose Julian
    Systems & control letters
    Vol. 56, num. 3, p. 197-205
    Date of publication: 2007-03
    Journal article

     Share Reference managers Reference managers Open in new window

  • Normal forms for rational difference equations with applications to the global periodicity problem

     Rubió-Massegú, J; Rubió Massegú, Josep; Mañosa Fernández, Víctor
    Journal of mathematical analysis and applications
    Vol. 332, num. 2, p. 896-918
    Date of publication: 2007-08
    Journal article

     Share Reference managers Reference managers Open in new window

  • Dynamics of the third order Lyness' difference equation

     Cima, A; Gasull, A; Mañosa Fernández, Víctor
    Journal of difference equations and applications
    Vol. 13, num. 10, p. 855-884
    Date of publication: 2007-10
    Journal article

    View View Open in new window  Share Reference managers Reference managers Open in new window

  • On the enveloping method and the existence of global Lyapunov functions

     Rubió-Massegú, J; Rubió Massegú, Josep; Mañosa Fernández, Víctor
    Journal of difference equations and applications
    Vol. 13, num. 11, p. 1029-1035
    Date of publication: 2007-11
    Journal article

     Share Reference managers Reference managers Open in new window

  • Global periodicity and complete integrability of discrete dynamical systems

     Cima, A; Gasull, A; Mañosa Fernández, Víctor
    Journal of difference equations and applications
    Vol. 12, num. 7, p. 697-716
    Date of publication: 2006-07
    Journal article

     Share Reference managers Reference managers Open in new window

  • Dynamics of some rational discrete dynamical systems via invariants

     Cima, A; Gasull, A; Mañosa Fernández, Víctor
    International journal of bifurcation and chaos
    Vol. 16, num. 3, p. 631-645
    Date of publication: 2006-05
    Journal article

     Share Reference managers Reference managers Open in new window

  • Dinàmica no lineal en dimensió baixa i atractors estranys

     Alseda Soler, Lluis; Pantazi, Chara; Delshams i Valdes, Amadeu; Mañosa Fernández, Víctor; Gutiérrez Serrés, Pere; Baldoma Barraca, Inmaculada Concepcion; Martinez-seara Alonso, Maria Teresa; Villanueva Castelltort, Jordi; Puig Sadurni, Joaquim
    Competitive project

     Share