Equidistribution results for geodesic flows

Details Equidistribution results for geodesic flows Equidistribution results for geodesic flows

2010-04-15

arxiv.org/abs/1004.2585v3

Mathematics

Dynamical Systems

25 pages

Scientific paper

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.

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