Large deviations, Gibbs measures and closed orbits for hyperbolic flows.

Mark Pollicott

Displaying similar documents to “Large deviations, Gibbs measures and closed orbits for hyperbolic flows.”

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Generic measures for geodesic flows on nonpositively curved manifolds

Yves Coudène, Barbara Schapira (2014)

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We study the generic invariant probability measures for the geodesic flow on connected complete nonpositively curved manifolds. Under a mild technical assumption, we prove that ergodicity is a generic property in the set of probability measures defined on the unit tangent bundle of the manifold and supported by trajectories not bounding a flat strip. This is done by showing that Dirac measures on periodic orbits are dense in that set. In the case of a compact surface, we...