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Singular solutions for a class of traveling wave equations arising in hydrodynamics
Geyer, Anna; Mañosa Fernández, Víctor
Date: 20150219
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Read the abstract View Share Reference managersWe give an exhaustive characterization of singular weak solutions for ordinary differential equations of the form $\ddot{u}\,u + \frac{1}{2}\dot{u}^2 + F'(u) =0$, where $F$ is an analytic function. Our motivation stems from the fact that in the context of hydrodynamics several prominent equations are reducible to an equation of this form upon passing to a moving frame. We construct peaked and cusped waves, fronts with finitetime decay and compact solitary waves. We prove that one cannot obtain peaked and compactly supported traveling waves for the same equation. In particular, a peaked traveling wave cannot have compact support and vice versa. To exemplify the approach we apply our results to the CamassaHolm equation and the equation for surface waves of moderate amplitude, and show how the different types of singular solutions can be obtained varying the energy level of the corresponding planar Hamiltonian systems. 
Lie symmetries of birational maps preserving genus 0 fibrations
Llorens, Mireia; Mañosa Fernández, Víctor
Date: 20150213
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Read the abstract View Share Reference managersWe prove that any planar birational integrable map, which preserves a fibration given by genus $0$ curves has a Lie symmetry and some associated invariant measures. The obtained results allow to study in a systematic way the global dynamics of these maps. Using this approach, the dynamics of several maps is described. In particular we are able to give, for particular examples, the explicit expression of the rotation number function, and the set of periods of the considered maps. 
Dynamics of integrable birational maps preserving genus 0 foliations
Llorens, Mireia; Mañosa Fernández, Víctor
Date: 20141003
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Read the abstract Access to the full text Share Reference managersPòster 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: 20141003
Presentation of work at congresses
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Spectral properties of the connectivity matrix and the SISepidemic threshold for midsize metapopulations
Juher Barrot, David; Mañosa Fernández, Víctor
Mathematical modeling of natural phenomena
Vol. 9, num. 2, p. 108120
DOI: 10.1051/mmnp/20149207
Date of publication: 20140424
Journal article
Read the abstract Access to the full text Share Reference managersWe 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 continuoustime equations of the model. In particular we show that the classical sufficient condition of instability for the diseasefree 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. 423437
DOI: 10.1080/10236198.2013.852187
Date of publication: 201403
Journal article
Read the abstract View Share Reference managersWe 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 2periodic points. We apply our results to several examples.
Postprint (author’s final draft) 
Periodic orbits of planar integrable birational maps
Gálvez Carrillo, Maria Immaculada; Mañosa Fernández, Víctor
Date: 20140214
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Read the abstract Access to the full text Share Reference managersA 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. 
Control, dinàmica i aplicacions
Ikhouane, Fayçal; Rossell Garriga, Josep Maria; Mañosa Fernández, Víctor; Pozo Montero, Francesc; Pujol Vazquez, Gisela; Palacios Quiñonero, Francisco; Rubió Massegú, Josep; Acho Zuppa, Leonardo; Vidal Segui, Yolanda; Ruiz Ordoñez, Magda Liliana; Mujica Delgado, Luis Eduardo; Mantecon Baena, Juan Antonio; Ismail Abdelkareem Moustafa, Mohammed; Bigorra Lopez, Laura; Alferez Baquero, Edwin Santiago; Tutivén Gálvez, Christian; Rodellar Benede, Jose Julian
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Integrability and nonintegrability of periodic nonautonomous Lyness recurrences
Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor
Dynamical systems: an international journal
Vol. 28, num. 4, p. 518538
DOI: 10.1080/14689367.2013.821103
Date of publication: 20131201
Journal article
Read the abstract Access to the full text Share Reference managersThis paper studies nonautonomous Lynesstype recurrences of the form x_{n+2} = (a_n + x_{n+1})/x n , where a_n is a kperiodic 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 nonautonomous Lynesstype recurrences of the form x n+2 = (a n + x n+1)/x n , where {a n } is a kperiodic 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. 
Global periodicity conditions for maps and recurrences via normal forms
Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor
International journal of bifurcation and chaos
Vol. 23, num. 11, p. 13501821135018218
DOI: 10.1142/S0218127413501824
Date of publication: 201311
Journal article
Read the abstract Access to the full text Share Reference managersWe 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 pperiodic, reducing the problem of finding the parameters for which the periodic cases appear to simple computations. We apply our results to several two and threedimensional classes of polynomial or rational maps. In particular, we find the global periodic cases for several Lynesstype 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 pperiodic, reducing the problem of finding the parameters for which the periodic cases appear to simple computations. We apply our results to several two and threedimensional classes of polynomial or rational maps. In particular, we find the global periodic cases for several Lynesstype recurrences.
Postprint (author’s final draft) 
Periodic orbits of planar integrable birational maps
Mañosa Fernández, Víctor
Date: 20130903
Report
Read the abstract Access to the full text Share Reference managersA 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. 
Periodic orbits of planar integrable birational maps
Mañosa Fernández, Víctor
International Workshop on Nonlinear Maps and their Applications
p. 4
Presentation's date: 20130903
Presentation of work at congresses
Read the abstract View Share Reference managersA 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. 
On the set of periods of the 2periodic Lyness’ Equation
Bastien, Guy; Mañosa Fernández, Víctor; Rogalski, Marc
Date: 20130725
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Read the abstract Access to the full text Share Reference managersWe study the periodic solutions of the nonautonomous 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 2pperiodic 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. 
Different approaches to the global periodicity problem
Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor; Mañosas, Francesc
Date: 20130725
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Read the abstract Access to the full text Share Reference managersLet F be a real or complex ndimensional 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 mdimensional 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 ndimensional 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 mdimensional 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. 
Basin of attraction of triangular maps with applications
Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor
Date: 20130725
Report
Read the abstract Access to the full text Share Reference managersWe 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 quasihomogeneous 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 2periodic points. Finally, we apply our results to a variety of examples, from particular cases of triangular systems to some planar quasihomogeneous maps, and some multiplicative and additive difference equations, as well. 
Spectral properties of the connectivity matrix and the SISepidemic threshold for midsize metapopulations
Juher Barrot, David; Mañosa Fernández, Víctor
Date: 20130510
Report
Read the abstract Access to the full text Share Reference managersWe 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 continuoustime equations of the model. In particular we show that the classical sufficient condition of instability for the diseasefree 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 continuoustime equations of the model. In particular we show that the classical sufﬁcient condition of instability for the diseasefree 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 
On periodic solutions of 2periodic Lyness' equations
Bastien, Guy; Mañosa Fernández, Víctor; Rogalski, Marc
International journal of bifurcation and chaos
Vol. 23, num. 4, p. 13500711135007118
DOI: 10.1142/S0218127413500715
Date of publication: 201304
Journal article
Read the abstract Access to the full text Share Reference managersWe study the existence of periodic solutions of the nonautonomous 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 5periodic. 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 5periodic. 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) 
Integrability and nonintegrability of periodic nonautonomous Lyness recurrences (revised and enlarged version)
Cima, Anna; Gasull, Armengol; Mañosa Fernández, Víctor
Date: 20121222
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Read the abstract Access to the full text Share Reference managersThis paper studies nonautonomous Lyness type recurrences of the form xn+2 = (an+xn+1)=xn, where fang is a kperiodic 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. 
Nonautonomous two periodic GumovskiMira difference equations
Cima, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor
International journal of bifurcation and chaos
Vol. 22, num. 11, p. 12502641125026414
DOI: 10.1142/S0218127412502641
Date of publication: 201212
Journal article
Read the abstract Access to the full text Share Reference managersWe consider two types of nonautonomous twoperiodic Gumovski–Mira difference equations. We show that while the corresponding autonomous recurrences are conjugated, the behavior of the sequences generated by the twoperiodic 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. 5556
Presentation's date: 20121004
Presentation of work at congresses
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Periodic orbits of integrable birational maps on the plane: blending dynamics and algebraic geometry, the Lyness' case
Bastien, Guy; Mañosa Fernández, Víctor; Rogalski, Marc
Date: 201210
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Read the abstract Access to the full text Share Reference managersContingut del Pòster presentat al congrés New Trends in Dynamical Systems 
A presentation on periodic solutions of 2periodic Lyness difference equations
Bastien, Guy; Mañosa Fernández, Víctor; Rogalski, Marc
Date: 20120727
Report
Read the abstract Access to the full text Share Reference managersPDF amb el contingut de la presentació al 18th ICDEA de Barcelona 
On periodic solutions of 2periodic Lyness difference equations
Bastien, Guy; Mañosa Fernández, Víctor; Rogalski, Marc
International Conference on Difference Equations and Applications
p. 49
Presentation's date: 20120727
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On 2 and 3periodic Lyness difference equations
Cima, Anna; Gasull, Armengol; Mañosa Fernández, Víctor
Journal of difference equations and applications
Vol. 18, num. 5, p. 849864
DOI: 10.1080/10236198.2010.524212
Date of publication: 20120511
Journal article
Read the abstract Access to the full text Share Reference managersWe describe the sequences {xn}n given by the nonautonomous secondorder Lyness difference equations xnþ2 ¼ ðan þ xnþ1Þ=xn, where {an}n is either a 2periodic 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, 18,5,849864 DOI:10.1080/10236198.2010.524212" 
Global periodicity conditions for maps and recurrences via Normal Forms
Cima, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor
Date: 20120504
Report
Read the abstract Access to the full text Share Reference managersWe 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 pperiodic, 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 
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. 587604
DOI: 10.3934/dcds.2012.32.587
Date of publication: 20120201
Journal article
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On periodic solutions of 2periodic Lyness difference equations
Bastien, Guy; Mañosa Fernández, Víctor; Rogalski, Marc
Date: 20120104
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Read the abstract Access to the full text Share Reference managersWe study the existence of periodic solutions of the nonautonomous 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 5periodic. 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
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Non autonomous 2periodic GumovskiMira difference equations
Cima, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor
Date: 20110601
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Read the abstract Access to the full text Share Reference managersWe consider two types of nonautonomous 2periodic GumovskiMira difference equations. We show that while the corresponding autonomous recurrences are conjugated, the behavior of the sequences generated by the 2periodic 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. 
Decentralized Hinfinity control of systems with information structure constraints
Rossell Garriga, Josep Maria; Palacios Quiñonero, Francisco; Luo Ren, Ningsu; Mañosa Fernández, Víctor
Workshop on Control Dynamics, Monitoring and Applications
p. 5762
Presentation's date: 20110207
Presentation of work at congresses
Read the abstract Access to the full text Share Reference managersThe paper deals with a class of continuoustime statedelayed uncertain systems considering Hinfinity control. The main objective is to design static output feedback controllers satisfying three requirements simultaneously: asymptotic stability for the closedloop 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) delayindependent approach is derived. A numerical example illustrates the effectiveness of the proposed method 
Integrability and nonintegrability of periodic nonautonomous Lyness recurrences
Cima, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor
Date: 20101222
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Read the abstract Access to the full text Share Reference managersThis paper studies nonautonomous Lyness type recurrences of the form x_{n+2}=(a_n+x_n)/x_{n+1}, where a_n is a kperiodic 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. 
On Poncelet's maps
Cima, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor
Computers & mathematics with applications
Vol. 60, num. 5, p. 14571464
DOI: 10.1016/j.camwa.2010.06.027
Date of publication: 20100808
Journal article
Read the abstract Access to the full text Share Reference managersGiven 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.
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Rational periodic sequences for the Lyness recurrence
Gasull Embid, Armengol; Mañosa Fernández, Víctor; Xarles Ribas, Xavier
Date: 20100430
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Read the abstract Access to the full text Share Reference managersConsider 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 1periodic and 5periodic sequences are easily obtained. We prove that for infinitely many positive values of $a,$ positive 9period 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 twoparameter 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. 
Dinámica, Atractores y Nolinealidad: Caos y Estabilidad
Mañosa Fernández, Víctor; Jorba ., Angel
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On two and three periodic Lyness difference equations
Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor
Date: 20091226
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Read the abstract Access to the full text Share Reference managersWe describe the sequences {x_n}_n given by the nonautonomous second order Lyness difference equations x_{n+2}=(a_n+x_{n+1})/x_n, where {a_n}_n is either a 2periodic or a 3periodic 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. 
On Poncelettype maps.
Mañosa Fernández, Víctor
International Conference on Difference Equations and Applications
p. 69
Presentation's date: 20091022
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CONTROL, DINÀMICA I APLICACIONS (CODALAB)
Mantecon Baena, Juan Antonio; Ikhouane, Fayçal; Mañosa Fernández, Víctor; Vidal Segui, Yolanda; Rubió Massegú, Josep; Acho Zuppa, Leonardo; Mujica Delgado, Luis Eduardo; Pozo Montero, Francesc; Pujol Vazquez, Gisela; Palacios Quiñonero, Francisco; Rossell Garriga, Josep Maria; Gharibnezhad, Fahit; Galvis Restrepo, Eduard; Tibaduiza Burgos, Diego Alexander; Ismail Abdelkareem Moustafa, Mohammed; Rodellar Benede, Jose Julian
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Identification of oneparameter bifurcations giving rise to periodic orbits, from their period function
Gasull Embid, Armengol; Mañosa Fernández, Víctor; Villadelprat Yagüe, Jordi
International Workshop on Dynamics and Control
Presentation's date: 20090601
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CONTROL DESCENTRALIZADO DE SISTEMAS EN RED A GRAN ESCALA CON INCERTIDUMBRES Y RETARDOS
Mañosa Fernández, Víctor; Palacios Quiñonero, Francisco; Rossell Garriga, Josep Maria
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On Poncelet's maps
Cima, A; Mañosa Fernández, Víctor; Gasull, A
Date: 200812
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Control descentralizado de sistemas en red a gran escala con incertidumbres y retardos (proyecto coordinado)
Mañosa Fernández, Víctor; Rossell Garriga, Josep Maria
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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: 20080901
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Estudio de sistemas dinámicos discretos vía ecuaciones diferenciales
Mañosa Fernández, Víctor
NoLineal 2008
Presentation's date: 20080616
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Some properties of the kdimensional Lyness' map
Cima, A; Gasull, A; Mañosa Fernández, Víctor
Journal of physics A. Mathematical and theoretical
Vol. 41, p. 8520585223
Date of publication: 200806
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A note on globally periodic maps and integrability
Mañosa Fernández, Víctor
Journal of difference equations and applications
Vol. 14, num. 6, p. 667670
Date of publication: 200806
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Studying discrete dynamical systems through differential equations
Cima, A; Gasull, A; Mañosa Fernández, Víctor
Journal of differential equations
Vol. 224, num. 3, p. 630648
Date of publication: 200802
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On the enveloping method and the existence of global Lyapunov functions
RubióMassegú, J; Rubió Massegú, Josep; Mañosa Fernández, Víctor
Journal of difference equations and applications
Vol. 13, num. 11, p. 10291035
Date of publication: 200711
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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. 855884
Date of publication: 200710
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Normal forms for rational difference equations with applications to the global periodicity problem
RubióMassegú, J; Rubió Massegú, Josep; Mañosa Fernández, Víctor
Journal of mathematical analysis and applications
Vol. 332, num. 2, p. 896918
Date of publication: 200708
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Dynamic properties of the hysteretic BoucWen model
Ikhouane, Fayçal; Mañosa Fernández, Víctor; Rodellar Benede, Jose Julian
Systems & control letters
Vol. 56, num. 3, p. 197205
Date of publication: 200703
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