On Birkhoff's conjecture about convex billiards

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Title:	On Birkhoff's conjecture about convex billiards
Author:	Delshams Valdés, Amadeu; Ramírez Ros, Rafael
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
Abstract:	Birkhoff conjectured that the elliptic billiard was the only integrable convex billiard. Here we prove a local version of this conjecture: any non-trivial symmetric entire perturbation of an elliptic billiard is non-integrable.
Subject(s):	-Topological dynamics -Hamiltonian systems -Measure theory -Ergodic theory -convex billiards -Birkhoff's conjecture -Dinàmica topològica -Hamilton, Sistemes de -Sistemes dinàmics diferenciables -Teoria ergòdica -Classificació AMS::28 Measure and integration::28D Measure-theoretic ergodic theory -Classificació AMS::37 Dynamical systems and ergodic theory::37K Infinite-dimensional Hamiltonian systems -Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems -Classificació AMS::37 Dynamical systems and ergodic theory::37B Topological dynamics
Rights:	Attribution-NonCommercial-NoDerivs 2.5 Spain http://creativecommons.org/licenses/by-nc-nd/2.5/es/
Document type:	Article
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