# Counting closed geodesics in globally hyperbolic maximal compact AdS 3-manifolds

@article{Glorieux2015CountingCG, title={Counting closed geodesics in globally hyperbolic maximal compact AdS 3-manifolds}, author={Olivier Glorieux}, journal={Geometriae Dedicata}, year={2015}, volume={188}, pages={63-101} }

We propose a definition for the length of closed geodesics in a globally hyperbolic maximal compact (GHMC) Anti-De Sitter manifold. We then prove that the number of closed geodesics of length less than R grows exponentially fast with R and the exponential growth rate is related to the critical exponent associated to the two hyperbolic surfaces coming from Mess parametrization. We get an equivalent of three results for quasi-Fuchsian manifolds in the GHMC setting: Bowen’s rigidity theorem of…

## 8 Citations

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We prove that the embedding of the Teichm\"uller space in the space of geodesic currents is totally linearly independent. As a corollary we get a rigidity result for the marked length spectrum of…

Entropy degeneration of globally hyperbolic maximal compact anti-de Sitter structures

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Using the parameterisation of the deformation space of GHMC anti-de Sitter structures on $S \times \mathbb{R}$ by the cotangent bundle of the Teichm\"uller space of $S$, we study how some geometric…

Critical exponent and Hausdorff dimension for quasi-Fuchsian AdS manifolds

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The aim of this article is to understand the geometry of limit sets in Anti-de Sitter space. We focus on a particular type of subgroups of $\mathrm{SO}(2,n)$ called quasi-Fuchsian groups (which are…

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