On the Growth of hyperbolic geodesics in rank 1 manifolds

We give a formula for the topological pressure of the geodesic flow of a compact rank 1 manifold in terms of the growth of the number of closed hyperbolic (rank 1) geodesics. We derive an equidistribution result for these geodesics with respect to equilibrium states. This generalize partially a resu...

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Bibliographic Details
Published inarXiv.org
Main Author Amroun, Abdelhamid
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 03.06.2013
Subjects
Geodesy
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Summary:We give a formula for the topological pressure of the geodesic flow of a compact rank 1 manifold in terms of the growth of the number of closed hyperbolic (rank 1) geodesics. We derive an equidistribution result for these geodesics with respect to equilibrium states. This generalize partially a result of G. Knieper \cite{kni} to non constant potentiels.
ISSN:2331-8422