CEMAPRE - Centre for Applied Mathematics and Economics

Financiador

Organização

Publicações

Billiards in generic convex bodies have positive topological entropy

Publication . Bessa, Mário; Del Magno, Gianluigi; Dias, João Lopes; Gaivão, José Pedro; Torres, Maria Joana

We show that there exists a C2-open dense set of convex bodies with smooth boundary whose billiard map exhibits a non-trivial hyperbolic basic set. As a consequence billiards in generic convex bodies have positive topological entropy and exponential growth of the number of periodic orbits.

2024Artigo científico

Acesso aberto

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Hyperbolicity through stable shadowing for generic geodesic flows

Publication . Bessa, Mário; Dias, João Lopes; Torres, Maria Joana

We prove that the closure of the closed orbits of a generic geodesic flow on a closed Riemannian n ≥ 2 dimensional manifold is a uniformly hyperbolic set if the shadowing property holds C2-robustly on the metric. We obtain analogous results using weak specification and the shadowing property allowing bounded time reparametrization.

2020Artigo científico

Acesso restrito

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Entidade financiadora

Fundação para a Ciência e a Tecnologia

Programa de financiamento

6817 - DCRRNI ID

Número da atribuição

UID/Multi/00491/2019