Data: 09/11/2016
Hora: 15:30h
Local: C116

Palestrante: Olivier Glorieux (IMPA)

Título: Critical exponent for globally hyperbolic, anti-de Sitter
manifolds.

Resumo: Critical exponent is a dynamical invariant measuring the exponential growth rate of number of closed geodesics. It has been extensively studied for hyperbolic manifolds. Anti-de Sitter manifolds are Lorentzian manifolds of constant curvature $-1$, it is the Lorentzian counterpart of the hyperbolic space. A subclass of Lorentzian manifolds, called globally hyperbolic, have nice properties making them look like quasi-Fuchsian hyperbolic manifolds. For globally hyperbolic, anti-de Sitter manifolds, we will explain how to define a notion of critical exponent and how it is related, as in the hyperbolic case, to the Hausdorff dimension of the limit set. We will not suppose any backgrounds
on Lorentzian geometry and recall all the basic definitions. Our aim is to explain similarities and differences between Anti-de Sitter geometry and hyperbolic geometry, from a dynamical point of view.