On Birkhoff's conjecture about convex billiards
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.
| Autores: | , |
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| Formato: | artículo |
| Fecha de publicación: | 1995 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/1189 |
| Acesso em linha: | https://hdl.handle.net/2117/1189 |
| Access Level: | acceso abierto |
| Palavra-chave: | 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 |
| Resumo: | 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. |
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