Abdelhamid Amroun
Published 2010-04-15, updated 2011-09-15Version 3
Using the works of Ma\~n\'e \cite{Ma} and Paternain \cite{Pat} we study the distribution of geodesic arcs with respect to equilibrium states of the geodesic flow on a closed manifold, equipped with a $\mathcal{C}^{\infty}$ Riemannian metric. We prove large deviations lower and upper bounds and a contraction principle for the geodesic flow in the space of probability measures of the unit tangent bundle. We deduce a way of approximating equilibrium states for continuous potentials.
Phase transitions for geodesic flows and the geometric potential
Pressures for geodesic flows of rank one manifolds
On the ergodicity of geodesic flows on surfaces without focal points
![QR code for arXiv:1004.2585 [math.DS]](http://oss.arxitics.com/images/favicon.svg)