Publicação
Expansiveness and hyperbolicity in convex billiards
| Resumo: | We say that a convex planar billiard table B is C²-stably expansive on a fixed open subset U of the phase space if its billiard map fB is expansive on the maximal invariant set ΛB,U = .Ո n∈Z f n B(U), and this property holds under C²-perturbations of the billiard table. In this note we prove for such billiards that the closure of the set of periodic points of fB in ΛB,U is uniformly hyperbolic. In addition, we show that this property also holds for a generic choice among billiards which are expansive |
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| Autores principais: | Bessa, Mário |
| Outros Autores: | Dias, José Lopes; Torres, Maria Joana |
| Assunto: | Convex Planar Billiards Hyperbolic Sets Expansiveness |
| Ano: | 2021 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade de Lisboa |
| Idioma: | inglês |
| Origem: | Repositório da Universidade de Lisboa |
| Resumo: | We say that a convex planar billiard table B is C²-stably expansive on a fixed open subset U of the phase space if its billiard map fB is expansive on the maximal invariant set ΛB,U = .Ո n∈Z f n B(U), and this property holds under C²-perturbations of the billiard table. In this note we prove for such billiards that the closure of the set of periodic points of fB in ΛB,U is uniformly hyperbolic. In addition, we show that this property also holds for a generic choice among billiards which are expansive |
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