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Displaying similar documents to “Invariant measures of the geodesic flow and measures at infinity on negatively curved manifolds”

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...

A characterization of harmonic measures on laminations by hyperbolic Riemann surfaces

Yuri Bakhtin, Matilde Martánez (2008)

Annales de l'I.H.P. Probabilités et statistiques

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ℒ denotes a (compact, nonsingular) lamination by hyperbolic Riemann surfaces. We prove that a probability measure on ℒ is harmonic if and only if it is the projection of a measure on the unit tangent bundle T 1 ℒ of ℒ which is invariant under both the geodesic and the horocycle flows.