Displaying similar documents to “Ergodicity of harmonic invariant measures for the geodesic flow on hyperbolic spaces.”

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.

Hyperbolic systems on nilpotent covers

Yves Coudene (2003)

Bulletin de la Société Mathématique de France

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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.

Absolute continuity, Lyapunov exponents and rigidity I: geodesic flows

Artur Avila, Marcelo Viana, Amie Wilkinson (2015)

Journal of the European Mathematical Society

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We consider volume-preserving perturbations of the time-one map of the geodesic flow of a compact surface with negative curvature. We show that if the Liouville measure has Lebesgue disintegration along the center foliation then the perturbation is itself the time-one map of a smooth volume-preserving flow, and that otherwise the disintegration is necessarily atomic.