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Hyperbolic systems on nilpotent covers

Yves Coudene — 2003

Bulletin de la Société Mathématique de France

We study the ergodicity of the weak and strong stable foliations of hyperbolic systems on nilpotent covers. Subshifts of finite type and geodesic flows on negatively curved manifolds are also considered.

Generic measures for geodesic flows on nonpositively curved manifolds

Yves CoudèneBarbara Schapira — 2014

Journal de l’École polytechnique — Mathématiques

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 get the following...

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