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TitleExpansiveness and hyperbolicity in convex billiards
Author(s)Bessa, Mário
Dias, João Lopes
Torres, M. J.
KeywordsConvex planar billiards
Hyperbolic sets
Issue date2021
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.
Publisher version
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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