Please use this identifier to cite or link to this item: https://hdl.handle.net/1822/75225

TitleExpansiveness and hyperbolicity in convex billiards
Author(s)Bessa, Mário
Dias, João Lopes
Torres, M. J.
KeywordsConvex planar billiards
Hyperbolic sets
Expansiveness
Issue date2021
PublisherSpringer
JournalRegular and Chaotic Dynamics
Abstract(s)We say that a convex planar billiard table B is C^2-stably expansive on a fixed open subset U of the phase space if its billiard map f_B is expansive on the maximal invariant set Λ_(B,U) = ∩_(n∈Z ) f_B^n(U), and this property holds under C^2 perturbations of the billiard table. In this note we prove for such billiards that the closure of the set of periodic points of f_B in Λ_(B,U) is uniformly hyperbolic. In addition we show that this property also holds for a generic choice among billiards which are expansive.
TypeArticle
URIhttps://hdl.handle.net/1822/75225
DOI10.1134/S1560354721060125
ISSN1560-3547
e-ISSN1468-4845
Publisher versionhttps://link.springer.com/article/10.1134/S1560354721060125
Peer-Reviewedyes
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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