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Positive topological entropy for semi-Riemannian geodesic flows

We consider a semi-Riemannian metric whose associated geodesic flow either contains a non-hyperbolic periodic orbit or has infinitely many hyperbolic periodic orbits. Under some conditions, we show that the metric can be C^2-perturbed such that the geodesic flow exhibits positive topological entropy, there are infinitely many non-lightlike closed geodesics, and their number grows exponentially with respect to t...

Positive topological entropy for semi-Riemannian geodesic flows

We consider a semi-Riemannian metric whose associated geodesic flow either contains a non-hyperbolic periodic orbit or has infinitely many hyperbolic periodic orbits. Under some conditions, we show that the metric can be perturbed such that the geodesic flow exhibits positive topological entropy, there are infinitely many non-lightlike closed geodesics, and their number grows exponentially with respect to the l...

Billiards in generic convex bodies have positive topological entropy

We show that there exists a C^2 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.

Billiards in generic convex bodies have positive topological entropy

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.

IgG4-related disease presenting as mass-like sclerosing mesenteritis

A Doença relacionada à IgG4 é uma entidade recentemente reconhecida que inclui um grupo de doenças fibroinflamatórias auto-imunes que apresentam características histologicas típicas. Pode afectar múltiplos órgãos, produzindo um amplo espectro de apresentações clínicas.A seleção dos métodos de imagem adequados é baseada nos sintomas do doente e no órgão em avaliação.O diagnóstico baseia-se na integração de achad...

Expansiveness and hyperbolicity in convex billiards

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 a...

Hyperbolic polygonal billiards close to 1-dimensional piecewise expanding maps

We consider polygonal billiards with collisions contracting the reflection angle towards the normal to the boundary of the table. In previous work, we proved that such billiards have a finite number of ergodic SRB measures supported on hyperbolic generalized attractors. Here we study the relation of these measures with the ergodic absolutely continuous invariant probabilities (acips) of the slap map, the 1-dime...

Expansiveness and hyperbolicity in convex billiards

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 f_B is expansive on the maximal invariant set Λ_{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 f_B in Λ_{B,U} is uniformly hyperbolic. In addition, we show that ...

Development of a Portuguese COVID-19 Imaging Repository and Database: Learning ...

Hyperbolicity through stable shadowing for generic geodesic flows

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.