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Critical exponent for globally hyperbolic, anti-de Sitter manifolds.
Olivier Glorieux (Luxembourg)
Aula Beltrami - Giovedì 26 Gennaio 2017 h.16:00
Abstract. 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 (Lorentzian) 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.
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