Equidistribution results for geodesic flows

Abstract

Using the works of Mañé \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.

arXiv comment25 pages

Cited by in corpus (1)

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