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1 to 50 of 149 results
  • A new approach to the vakonomic mechanics

     Llibre Saló, Jaume; Ramirez Ros, Rafael; Sadovskaia Nurimanova, Natalia
    Nonlinear dynamics
    Vol. 78, num. 3, p. 2219-2247
    DOI: 10.1007/s11071-014-1554-3
    Date of publication: 2014-11-01
    Journal article

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    The aim of this paper was to show that the Lagrange-d'Alembert and its equivalent the Gauss and Appel principle are not the only way to deduce the equations of motion of the nonholonomic systems. Instead of them we consider the generalization of the Hamiltonian principle for nonholonomic systems with non-zero transpositional relations. We apply this variational principle, which takes into the account transpositional relations different from the classical ones, and we deduce the equations of motion for the nonholonomic systems with constraints that in general are nonlinear in the velocity. These equations of motion coincide, except perhaps in a zero Lebesgue measure set, with the classical differential equations deduced with the d'Alembert-Lagrange principle. We provide a new point of view on the transpositional relations for the constrained mechanical systems: the virtual variations can produce zero or non-zero transpositional relations. In particular, the independent virtual variations can produce non-zero transpositional relations. For the unconstrained mechanical systems, the virtual variations always produce zero transpositional relations. We conjecture that the existence of the nonlinear constraints in the velocity must be sought outside of the Newtonian mechanics. We illustrate our results with examples.

  • On Cayley conditions for billiards inside ellipsoids

     Ramirez Ros, Rafael
    Nonlinearity
    Vol. 27, num. 5, p. 1003-1028
    DOI: 10.1088/0951-7715/27/5/1003
    Date of publication: 2014-05
    Journal article

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    Billiard trajectories inside an ellipsoid of Rn are tangent to n-1 quadrics of the pencil of confocal quadrics determined by the ellipsoid. The quadrics associated with periodic trajectories verify certain algebraic conditions. Cayley found them for the planar case. Dragovic and Radnovic generalized them to any dimension. We rewrite the original matrix formulation of these generalized Cayley conditions as a simpler polynomial one. We find several algebraic relations between caustic parameters and ellipsoidal parameters that give rise to non-singular periodic trajectories. These relations become remarkably simple when the elliptic period is minimal. We study the caustic types, the winding numbers and the ellipsoids of such minimal periodic trajectories. We also describe some non-minimal periodic trajectories

  • Sistemes dinàmics de la UPC

     Baldoma Barraca, Inmaculada Concepcion; Delshams i Valdes, Amadeu; Fedorov Kuzmin, Yury; Guillamon Grabolosa, Antoni; Gutiérrez Serrés, Pere; Huguet Casades, Gemma; Lazaro Ochoa, Jose Tomas; Martin De La Torre, Pablo; Masdemont Soler, Josep Joaquim; Olle Torner, Maria Mercedes; Pacha Andujar, Juan Ramon; Pantazi, Chara; Puig Sadurni, Joaquim; Ramirez Ros, Rafael; Roldan Gonzalez, Pablo; Villanueva Castelltort, Jordi; Castejon i Company, Oriol; Tamarit Sariol, Anna; Simon Lopez, Adria; Sanchez Martin, Patricia; Bonet Reves, Carles; Sanchez Cuartielles, Joan Pau; Paita, Fabrizio; Martinez-seara Alonso, Maria Teresa
    Competitive project

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  • Non-persistence of resonant caustics in perturbed elliptic billiards

     Pinto de Carvalho, Sonia; Ramirez Ros, Rafael
    Ergodic theory and dynamical systems
    Vol. 33, num. 6, p. 1876-1890
    DOI: 10.1017/S0143385712000417
    Date of publication: 2013-12
    Journal article

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    A caustic of a billiard table is a curve such that any billiard trajectory, once tangent to the curve, stays tangent after every reflection at the boundary. When the billiard table is an ellipse, any non-singular billiard trajectory has a caustic, which can be either a confocal ellipse or a confocal hyperbola. Resonant caustics - those whose tangent trajectories are closed polygons - are destroyed under generic perturbations of the billiard table. We prove that none of the resonant elliptical caustics persists under a large class of explicit perturbations of the original ellipse. This result follows from a standard Melnikov argument and the analysis of the complex singularities of certain elliptic functions. Copyright © 2012 Cambridge University Press.

  • Brazilian–European Partnership in Dynamical Systems

     Ramirez Ros, Rafael; Lazaro Ochoa, Jose Tomas; Delshams i Valdes, Amadeu; Martinez-seara Alonso, Maria Teresa
    Competitive project

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  • Billiards with a given number of (k,n)-orbits

     Pinto de Carvalho, Sonia; Ramirez Ros, Rafael
    Chaos
    Vol. 22, num. 2, p. 1-6
    DOI: 10.1063/1.3697986
    Date of publication: 2012-04-04
    Journal article

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  • Classification of symmetric periodic trajectories in ellipsoidal billiards

     Casas, Pablo S.; Ramirez Ros, Rafael
    Chaos
    Vol. 22, num. 2012, p. 1-26
    DOI: 10.1063/1.4706003
    Date of publication: 2012-04-04
    Journal article

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  • On the 16th Hilbert problem for limit cycles on nonsingular algebraic curves

     Llibre Saló, Jaume; Ramirez Ros, Rafael; Sadovskaia Nurimanova, Natalia
    Journal of differential equations
    Vol. 250, num. 2, p. 983-999
    DOI: 10.1016/j.jde.2010.06.009
    Date of publication: 2011-01-15
    Journal article

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    We give an upper bound for the maximum number N of algebraic limit cycles that a planar polynomial vector field of degree n can exhibit if the vector field has exactly k nonsingular irreducible invariant algebraic curves. Additionally we provide sufficient conditions in order that all the algebraic limit cycles are hyperbolic. We also provide lower bounds for N.

  • The Frequency Map for Billiards inside Ellipsoids

     Sánchez Casas, José Pablo; Ramirez Ros, Rafael
    SIAM journal on applied dynamical systems
    Vol. 10, num. 1, p. 278-324
    DOI: 10.1137/10079389X
    Date of publication: 2011
    Journal article

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  • Access to the full text
    El método de Poincaré  Open access

     Ramirez Ros, Rafael
    Date of publication: 2011
    Book chapter

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    Estas notas corresponden a las exposiciones presentadas en el \emph{Primer Seminario de Integrabilidad}, dentro de lo que se denomina \emph{Aula de Sistemas Din\'amicos}. Durante este evento se realizaron seis conferencias, todas presentadas por miembros del grupo de Sistemas Din\'amicos de la UPC. El programa desarrollado fue el siguiente:\\ \begin{center} AULA DE SISTEMAS DIN\'AMICOS \end{center} \begin{center} \texttt{http://www.ma1.upc.es/recerca/seminaris/aulasd-cat.html} \end{center} \begin{center} SEMINARIO DE INTEGRABILIDAD \end{center} \begin{center} Martes 29 y Mi\'ercoles 30 de marzo de 2005\\ Facultad de Matem\'aticas y Estad\'{\i}stica, UPC\\ Aula: Seminario 1 \end{center} \bigskip \begin{center} PROGRAMA Y RES\'UMENES \end{center} {\bf Martes 29 de marzo} \begin{itemize} \item 15:30. Juan J. Morales-Ruiz. \emph{El problema de la integrabilidad en Sistemas Din\'amicos} \medskip {\bf Resumen.} En esta presentaci\'on se pretende dar una idea de conjunto, pero sin entrar en detalles, sobre las diversas nociones de integrabilidad, asociadas a nombres de matem\'aticos tan ilustres como Liouville, Galois-Picard-Vessiot, Lie, Darboux, Kowalevskaya, Painlev\'e, Poincar\'e, Kolchin, Lax, etc. Adem\'as tambi\'en mencionaremos la revoluci\'on que supuso en los a\~nos sesenta del siglo pasado el descubrimiento de Gardner, Green, Kruskal y Miura sobre un nuevo m\'etodo para resolver en algunos casos determinadas ecuaciones en derivadas parciales. \medskip \item 16:00. David G\'omez-Ullate. \emph{Superintegrabilidad, pares de Lax y modelos de $N-$cuerpos en el plano} \medskip {\bf Resumen.} Introduciremos algunas t\'ecnicas cl\'asicas para construir modelos de N-cuerpos integrables, como los pares de Lax o la din\'amica de los ceros de un polinomio. Revisaremos la noci\'on de integrabilidad Liouville y superintegrabilidad, y discutiremos un nuevo m\'etodo debido a F. Calogero para contruir modelos de N-cuerpos en el plano con muchas \'orbitas peri\'odicas. La exposici\'on se acompa\~nar\'a de animaciones del movimiento de los cuerpos, y se plantear\'an algunos problemas abiertos. \medskip \item 17:00. Pausa \medskip \item 17:30. Yuri Fedorov. \emph{An\'alisis de Kovalevskaya--Painlev\'e y Sistemas Algebraicamente Integrables} \medskip {\bf Resumen.} Muchos sistemas integrables poseen una propiedad remarcable: todas sus soluciones son funciones meromorfas del tiempo como una variable compleja. Tal comportamiento, que se refiere como propiedad de Kovalevskaya-Painleve (KP) y que se usa frecuentemente como una ensayo de integrabilidad, no es accidental y tiene unas ra\'{\i}ces geom\'etricas profundas. En esta charla describiremos una clase de tales sistemas (conocidos como los sistemas algebraicamente integrables) y subrayaremos sus propiedades geom\'etricas principales que permiten predecir la estructura de las soluciones complejas y adem\'as encontrarlas expl\'{\i}citamente. Eso lo ilustraremos con algunos sistemas de la mec\'anica cl\'asica. Tambi\'en mencionaremos unas generalizaciones \'utiles de la noci\'on de integrabilidad algebraica y de la propiedad KP. \end{itemize} \medskip {\bf Mi\'ercoles 30 de marzo} \begin{itemize} \item 15:30. Rafael Ram\'{\i}rez-Ros. \emph{El m\'etodo de Poincar\'e} \medskip {\bf Resumen.} Dado un sistema Hamiltoniano aut\'onomo cercano a completamente integrable Poincar\'e prob\'o que, en general, no existe ninguna integral primera adicional uniforme en el par\'ametro de perturbaci\'on salvo el propio Hamiltoniano. Esbozaremos las ideas principales del m\'etodo de prueba y comentaremos algunas extensiones y generalizaciones. \newpage \item 16:30. Chara Pantazi. \emph{El M\'etodo de Darboux} \medskip {\bf Resumen.} Darboux, en 1878, present\'o su m\'etodo para construir integrales primeras de campos vectoriales polinomiales utilizando sus curvas invariantes algebraicas. En esta exposici\'on presentaremos algunas extensiones del m\'etodo cl\'asico de Darboux y tambi\'en algunas aplicaciones. \medskip \item 17:30. Pausa \medskip \item 18:00. Juan J. Morales-Ruiz. \emph{M\'etodos recientes para detectar la no integrabilidad} \medskip {\bf Resumen.} En 1982 Ziglin utiliza la estructura de la ecuaci\'on en variaciones de Poincar\'e (sobre una curva integral particular) como una herramienta fundamental para detectar la no integrabilidad de un sistema Hamiltoniano. En esta charla se pretende dar una idea de esta aproximaci\'on a la no integrabilidad, junto con t\'ecnicas m\'as recientes que involucran la teor\'{\i}a de Galois de ecuaciones diferenciales lineales, haciendo \'enfasis en los ejemplos m\'as que en la teor\'{\i}a general. Ilustraremos estos m\'etodos con resultados sobre la no integrabilidad de algunos problemas de $N$ cuerpos en Mec\'anica Celeste. \end{itemize}

  • Stability of the phase motion in microtrons

     Koubychine Merkulov, Youri Alexandrovich; Larreal Barreto, Oswaldo; Ramirez Ros, Rafael; Martinez-seara Alonso, Maria Teresa
    Dual Year Russia-Spain
    Presentation of work at congresses

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  • The frequency map for billiards inside ellipsoids

     Ramirez Ros, Rafael; Sánchez Casas, José Pablo
    Emerging Topics in Dynamical Systems and Partial Differential Equations DSPDEs'10/Joint SIAM/RSME-SCM-SEMA Meeting
    Presentation's date: 2010-06-03
    Presentation of work at congresses

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  • The frequency map for billiards inside ellipsoids

     Ramirez Ros, Rafael; Sánchez Casas, José Pablo
    Date: 2010-06
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  • Access to the full text
    The frequency map for billiards inside ellipsoids  Open access

     Ramirez Ros, Rafael; Sánchez Casas, José Pablo
    Date: 2010-04
    Report

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    The billiard motion inside an ellipsoid Q Rn+1 is completely integrable. Its phase space is a symplectic manifold of dimension 2n, which is mostly foliated with Liouville tori of dimension n. The motion on each Liouville torus becomes just a parallel translation with some frequency ! that varies with the torus. Besides, any billiard trajectory inside Q is tangent to n caustics Q 1 ; : : : ;Q n, so the caustic parameters = ( 1; : : : ; n) are integrals of the billiard map. The frequency map 7! ! is a key tool to understand the structure of periodic billiard trajectories. In principle, it is well-defined only for nonsingular values of the caustic parameters. We present four conjectures, fully supported by numerical experiments. The last one gives rise to some lower bounds on the periods. These bounds only depend on the type of the caustics. We describe the geometric meaning, domain, and range of !. The map ! can be continuously extended to singular values of the caustic parameters, although it becomes “exponentially sharp” at some of them. Finally, we study triaxial ellipsoids of R3. We compute numerically the bifurcation curves in the parameter space on which the Liouville tori with a fixed frequency disappear. We determine which ellipsoids have more periodic trajectories. We check that the previous lower bounds on the periods are optimal, by displaying periodic trajectories with periods four, five, and six whose caustics have the right types. We also give some new insights for ellipses of R2.

  • On the 16th Hilbert problem for algebraic limit cycles

     Llibre Saló, Jaume; Ramirez Ros, Rafael; Sadovskaia Nurimanova, Natalia
    Journal of differential equations
    Vol. 248, num. 6, p. 1401-1409
    DOI: 10.1016/j.jde.2009.11.023
    Date of publication: 2010-03-15
    Journal article

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    For a polynomial planar vector field of degree n ≥ 2 with generic invariant algebraic curves we show that the maximum number of algebraic limit cycles is 1 + (n − 1)(n − 2)/2 when n is even, and (n − 1)(n − 2)/2 when n is odd. Furthermore, these upper bounds are reached.

  • DINAMICA ASOCIADA A CONEXIONES ENTRE OBJETOS INVARIANTES, ASTRODINÁMICA, NEUROCIENCIA Y OTRAS APLICACIONES

     Blazquez Sanz, David; Olive Farre, Maria del Carme; Gomez-Ullate Oteiza, David; Morales Ruiz, Juan Jose; Canalias Vila, Elisabet; Martinez-seara Alonso, Maria Teresa; Baldoma Barraca, Inmaculada Concepcion; Fedorov Kuzmin, Yury; Garcia Taberner, Laura; Guardia Munarriz, Marcel; Guillamon Grabolosa, Antoni; Gonchenko, Marina; Gutiérrez Serrés, Pere; Lazaro Ochoa, Jose Tomas; Luque Jiménez, Alejandro; Martin De La Torre, Pablo; Masdemont Soler, Josep Joaquim; Olle Torner, Maria Mercedes; Pacha Andujar, Juan Ramon; Pantazi, Chara; Puig Sadurni, Joaquim; Ramirez Ros, Rafael; Roldan Gonzalez, Pablo; Villanueva Castelltort, Jordi; Tamarit, Anna; Olivé Farré, Carme; Morales Ruiz, Juan José; Larreal Barreto, Oswaldo José; Huguet Casades, Gemma; Gómez-Ullate Oteiza, David; Acosta Humanez, Primitivo Belen; Benita Bordes, Jose Manuel; Basak, Inna; Blázquez Sanz, David; de la Llave Canosa, Rafael; de la Rosa Ibarra, Abraham; Delshams i Valdes, Amadeu
    Competitive project

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  • The frequency map for billiards inside ellipsoids

     Ramirez Ros, Rafael; Sánchez Casas, José Pablo
    Date: 2009-12
    Report

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  • SISTEMES DINAMICS DE LA UPC

     Fedorov Kuzmin, Yury; Villanueva Castelltort, Jordi; de la Llave Canosa, Rafael; Lazaro Ochoa, Jose Tomas; Olive Farre, Maria del Carme; Guardia Munarriz, Marcel; Benita Bordes, Jose Manuel; Puig Sadurni, Joaquim; Canalias Vila, Elisabet; Martin De La Torre, Pablo; Guillamon Grabolosa, Antoni; Larreal Barreto, Oswaldo José; Luque Jiménez, Alejandro; Gomez-Ullate Oteiza, David; Pantazi, Chara; de la Rosa Ibarra, Abraham; Martinez-seara Alonso, Maria Teresa; Masdemont Soler, Josep Joaquim; Blazquez Sanz, David; Baldoma Barraca, Inmaculada Concepcion; Gutiérrez Serrés, Pere; Olle Torner, Maria Mercedes; Ramirez Ros, Rafael; Pacha Andujar, Juan Ramon; Roldan Gonzalez, Pablo; Morales Ruiz, Juan Jose; Huguet Casades, Gemma; Gonchenko, Marina; Acosta Humanez, Primitivo Belen; Delshams i Valdes, Amadeu
    Competitive project

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  • Separatrix splitting in 3D volume-preserving maps

     Lomeli, Hector E.; Ramirez Ros, Rafael
    SIAM journal on applied dynamical systems
    Vol. 7, num. 4, p. 1527-1557
    DOI: 10.1137/080713173
    Date of publication: 2008-12
    Journal article

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  • On the determination of the potential function from given orbits

     Alboul, L; Mencia, J; Ramirez Ros, Rafael; Sadovskaia Nurimanova, Natalia
    Czechoslovak mathematical journal
    Vol. 58, num. 3, p. 799-821
    DOI: 10.1007/s10587-008-0052-5
    Date of publication: 2008-09
    Journal article

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  • Review de l'article: Canonical Melnikov theory for diffeomorphisms. Autors: Lomelí, H. E.; Meiss, J. D.; Ramírez-Ros, R

     Meiss, James D; Ramirez Ros, Rafael; Meiss, J.D.
    Mathematical reviews
    Date of publication: 2008-04
    Journal article

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  • Canonical Melnikov theory for diffeomorphisms

     Lomelí, Héctor E.; Meiss, James D; Ramirez Ros, Rafael
    Nonlinearity
    Vol. 21, p. 485-508
    DOI: 10.1088/0951-7715/21/3/007
    Date of publication: 2008-03
    Journal article

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  • Assessment of active principle in microcapsules applied by pad-dry systems

     Valldeperas Morell, Jose; Lis Arias, Manuel Jose; Navarro Viciana, Juan Antonio; Cebrian Diaz, Juan Alfonso; Marti Gelabert, Meritxell; Ramirez Ros, Rafael; Coderch Negra, Luisa; Parra Juez, José Luis
    IFATCC International Congress
    Presentation of work at congresses

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  • Assessment of active principle in microcapsules applied by pad-dry sistems on different textile substrates

     Lis Arias, Manuel Jose; Valldeperas Morell, Jose; Marti Gelabert, Meritxell; Ramirez Ros, Rafael; Cebrian Diaz, Juan Alfonso; Navarro Viciana, Juan Antonio; Carreras Parera, Nuria; Coderch Negra, Luisa; Parra Juez, José Luis
    Mediterranean Congress of Chemical Engineering
    Presentation of work at congresses

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  • ¿ Is it possible to solve the Dynamics Problem Inside the Configuration Space?

     Ramirez Ros, Rafael; Sadovskaia Nurimanova, Natalia
    Date: 2007-09
    Report

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  • Development of a tool for calculating the effects of PV-systems connected to a low voltage grid

     Perelló, X; Sumper, Andreas; Ramirez Ros, Rafael; Sudria Andreu, Antoni; Villafafila Robles, Roberto; González, C
    19th International Conference on Electricity Distribution.
    p. 1-5
    Presentation of work at congresses

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  • Vehicles to obtain smart textiles with ceramides for sensitive skin

     Marti Gelabert, Meritxell; Lis Arias, Manuel Jose; Navarro Viciana, Juan Antonio; Ramirez Ros, Rafael; Coderch Negra, Luisa; Valldeperas Morell, Jose; Parra Juez, José Luis
    International Conference and Exhibition on Healthcare and Medical Textiles
    p. 1-8
    Presentation of work at congresses

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  • On wind power integration into electrical power system: Spain vs. Denmark

     Villafafila Robles, Roberto; Sumper, Andreas; Suwannarat, A; Bak-Jensen, B; Ramirez Ros, Rafael; Gomis Bellmunt, Oriol; Sudria Andreu, Antoni; Ramirez Pisco, Rodrigo
    International Conference on Renewable Energies and Power Quality
    p. 1-8
    Presentation of work at congresses

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  • On the number of limit cycles of the liénard equation

     Sadovskaia Nurimanova, Natalia; Ramirez Ros, Rafael
    Date: 2006-10
    Report

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  • Cartesian Aporoach for Nonholonomic System

     Ramirez Ros, Rafael; Sadovskaia Nurimanova, Natalia
    Date: 2006-10
    Report

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  • Development of a Tool for Calculating the Effects of Pvsystems Connected to a Low Voltage Grid

     Sumper, Andreas; Sudria Andreu, Antoni; Villafafila Robles, Roberto; Perelló, X; Ramirez Ros, Rafael; Chindris, Mircea
    Date of publication: 2006-06
    Book chapter

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  • On the number of limit cycles of the lienard equation.

     Ramirez Ros, Rafael; Sadovskaia Nurimanova, Natalia
    Date: 2006-05
    Report

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  • Frontier methodology to fix quality goals in electrical energy distribution companies Grid

     Sudria Andreu, Antoni; Sumper, Andreas; Bergas Jane, Joan Gabriel; Villafafila Robles, Roberto; Ramirez Ros, Rafael
    Date of publication: 2006-04
    Book chapter

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  • On periodic orbits of billiards inside perturbed circular tables

     Ramirez Ros, Rafael
    Carles Simó Fest (60th birthday). Conference on Dynamical Systems
    Presentation of work at congresses

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  • Mitigation of Capacitor Bank Energization Harmonic Transients

     Cipcigan, L; Chindris, Mircea; Rull Duran, Joan; Rusu, A; Sumper, Andreas; Ramirez Ros, Rafael; Alves, R; Ramirez Pisco, Rodrigo
    2006 IEEE PES Transmission & Distribution Latin Ameria
    p. 1-5
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  • Development of a Tool for Calculating the Effects of Pvsystems Connected to a Low Voltage Grid

     Perelló, X; Sumper, Andreas; Sudria Andreu, Antoni; Ramirez Ros, Rafael; Villafafila Robles, Roberto; Chindris, Mircea; Ramirez Pisco, Rodrigo
    IEEE Energy Conversion Congress and Exposition
    p. 1-5
    Presentation of work at congresses

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  • Break up of resonat invariant curves in billiards and dual billiards associated to perturbed circular tables

     Ramirez Ros, Rafael
    Physica. D, Nonlinear phenomena
    Vol. 214, num. 1, p. 78-87
    Date of publication: 2006-01
    Journal article

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  • Exponentially small separatrix splittings and almost invisible homoclinic bifurcations in some billiard tables

     Ramirez Ros, Rafael
    Physica. D, Nonlinear phenomena
    Vol. 210, num. 3-4, p. 149-179
    Date of publication: 2005-10
    Journal article

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  • Indices de continuidad en redes de distribución y su mejora

     Sudria Andreu, Antoni; Sumper, Andreas; Ramirez Ros, Rafael; Villafafila Robles, Roberto; Chindris, Mircea
    Date of publication: 2005-06
    Book chapter

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  • Retribución de la distribución de energía eléctrica en España. Caso actual vs. Yardstick Competition.

     Sudria Andreu, Antoni; Bergas Jane, Joan Gabriel; Ramirez Ros, Rafael; Tevar, G
    Date of publication: 2005-06
    Book chapter

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  • Indices de continuidad en redes de distribución y su mejora

     Sumper, Andreas; Sudria Andreu, Antoni; Ramirez Ros, Rafael; Villafafila Robles, Roberto; Chindris, Mircea; Ramirez Pisco, Rodrigo
    9th Spanish Portuguese Congress on Electrical Engineering
    p. 275-276
    Presentation of work at congresses

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  • Retribución de la distribución de energía eléctrica en España. Caso actual vs. Yardstick Competition

     Ramirez Ros, Rafael; Sudria Andreu, Antoni; Bergas Jane, Joan Gabriel; Tevar, G
    9th Spanish Portuguese Congress on Electrical Engineering
    p. 277-278
    Presentation of work at congresses

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  • Persistence of homoclinic orbits for billiards inside perturbed ellipsoids

     Ramirez Ros, Rafael
    AIMS Fifth International Conference on Dynamical Systems and Differential equations
    Presentation's date: 2004-06-18
    Presentation of work at congresses

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  • Trayectorias homoclínicas de billares dentro de elipsoides perturbados

     Ramirez Ros, Rafael
    Non lineal 2004
    Presentation's date: 2004-06-03
    Presentation of work at congresses

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  • Persistence of homoclinic orbits for billiards and twist maps

     Bolotin, S; Delshams i Valdes, Amadeu; Ramirez Ros, Rafael
    Nonlinearity
    Vol. 17, num. 4, p. 757-783
    Date of publication: 2004-04
    Journal article

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  • Trayectorias homoclínicas de billares dentro de elipsoides perturbados

     Ramirez Ros, Rafael; Bolotín, S; Delshams i Valdes, Amadeu
    Non lineal 2004
    p. 85
    Presentation of work at congresses

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