Displaying similar documents to “On the discrete Godbillon-Vey invariant and Dehn surgery on geodesic flows”

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.

Continuity of the bending map

Cyril Lecuire (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

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The bending map of a hyperbolic 3 -manifold maps a convex cocompact hyperbolic metric on a 3 -manifold with boundary to its bending measured geodesic lamination. As proved in [KeS] and [KaT], this map is continuous. In the present paper we study the extension of this map to the space of geometrically finite hyperbolic metrics. We introduce a relationship on the space of measured geodesic laminations and show that the quotient map obtained from the bending map is continuous.