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Persistence of homoclinic orbits for billiards and twist maps
dc.contributor.author | Bolotin, S. |
dc.contributor.author | Delshams Valdés, Amadeu |
dc.contributor.author | Ramírez Ros, Rafael |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I |
dc.date.accessioned | 2007-05-04T16:10:23Z |
dc.date.available | 2007-05-04T16:10:23Z |
dc.date.created | 2003 |
dc.date.issued | 2003 |
dc.identifier.uri | http://hdl.handle.net/2117/874 |
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. |
dc.format.extent | 29 |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 2.5 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/2.5/es/ |
dc.subject.lcsh | Differentiable dynamical systems |
dc.subject.lcsh | Hamiltonian systems |
dc.subject.other | homoclinic orbits |
dc.subject.other | billiards |
dc.subject.other | twist maps |
dc.title | Persistence of homoclinic orbits for billiards and twist maps |
dc.type | Article |
dc.subject.lemac | Sistemes dinàmics diferenciables |
dc.subject.lemac | Hamilton, Sistemes de |
dc.contributor.group | Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions |
dc.subject.ams | Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems |
dc.subject.ams | Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory |
dc.subject.ams | Classificació AMS::37 Dynamical systems and ergodic theory::37E Low-dimensional dynamical systems |
dc.rights.access | Open Access |
local.personalitzacitacio | true |
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