Displaying similar documents to “Mather measures and the Bowen–Series transformation”

Generic measures for geodesic flows on nonpositively curved manifolds

Yves Coudène, Barbara Schapira (2014)

Journal de l’École polytechnique — Mathématiques

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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...

The return sequence of the Bowen-Series map for punctured surfaces

Manuel Stadlbauer (2004)

Fundamenta Mathematicae

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For a non-compact hyperbolic surface M of finite area, we study a certain Poincaré section for the geodesic flow. The canonical, non-invertible factor of the first return map to this section is shown to be pointwise dual ergodic with return sequence (aₙ) given by aₙ = π/(4(Area(M) + 2π)) · n/(log n). We use this result to deduce that the section map itself is rationally ergodic, and that the geodesic flow associated to M is ergodic with respect to the...