Persistence of homoclinic orbits for billiards and twist maps

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To access the full text documents, please follow this link: http://hdl.handle.net/2117/874

dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.contributor	Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.contributor.author	Bolotin, S.
dc.contributor.author	Delshams Valdés, Amadeu
dc.contributor.author	Ramírez Ros, Rafael
dc.date	2003
dc.identifier.uri	http://hdl.handle.net/2117/874
dc.language.iso	eng
dc.rights	Attribution-NonCommercial-NoDerivs 2.5 Spain
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	http://creativecommons.org/licenses/by-nc-nd/2.5/es/
dc.subject	Differentiable dynamical systems
dc.subject	Hamiltonian systems
dc.subject	homoclinic orbits
dc.subject	billiards
dc.subject	twist maps
dc.subject	Sistemes dinàmics diferenciables
dc.subject	Hamilton, Sistemes de
dc.subject	Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
dc.subject	Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory
dc.subject	Classificació AMS::37 Dynamical systems and ergodic theory::37E Low-dimensional dynamical systems
dc.title	Persistence of homoclinic orbits for billiards and twist maps
dc.type	info:eu-repo/semantics/article
dc.description.abstract	We consider the billiard motion inside a C2-small perturbation of a ndimensional ellipsoid Q with a unique major axis. The diameter of the ellipsoid Q is a hyperbolic two-periodic trajectory whose stable and unstable invariant manifolds are doubled, so that there is a n-dimensional invariant set W of homoclinic orbits for the unperturbed billiard map. The set W is a stratified set with a complicated structure. For the perturbed billiard map the set W generically breaks down into isolated homoclinic orbits. We provide lower bounds for the number of primary homoclinic orbits of the perturbed billiard which are close to unperturbed homoclinic orbits in certain strata of W. The lower bound for the number of persisting primary homoclinic billiard orbits is deduced from a more general lower bound for exact perturbations of twist maps possessing a manifold of homoclinic orbits.

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