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Advisor(s)
Abstract(s)
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
Description
Keywords
Convex Planar Billiards Hyperbolic Sets Expansiveness
Pedagogical Context
Citation
Bessa, Mário; José Lopes Dias and Maria Joana Torres .(2021). “Expansiveness and hyperbolicity in convex billiards”. Regular and Chaotic Dynamics, Vol 26, No. 6: pp. 756-762. (Search PDF in 2023)
Publisher
Springer Nature