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arXiv · 1110.2365

Absolute continuity, Lyapunov exponents and rigidity I : geodesic flows

Artur Avila·Marcelo Viana·Amie Wilkinson
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Abstract

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.

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Artur Avila, Marcelo Viana, Amie Wilkinson. 2011-10-14. Absolute continuity, Lyapunov exponents and rigidity I : geodesic flows. https://arxiv.org/abs/1110.2365

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