Geometric and ergodic properties of the stable foliation

We classify reversible measures for the stable foliation on manifolds which are infinite covers of compact negatively curved manifolds. We extend the known results from hyperbolic surfaces to varying curvature and to all dimensions.

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.

Ergodic theory, semisimple Lie groups and foliations by manifolds of negative curvature

Robert J. Zimmer (1982)

Publications Mathématiques de l'IHÉS

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Invariant measures for a diffeomorphism which expands the leaves of a foliation

David Ruelle (1978)

Publications Mathématiques de l'IHÉS

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