Absolute continuity, Lyapunov exponents and rigidity I : geodesic flows
Dynamical Systems
2011-10-17 v2
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.
Keywords
Cite
@article{arxiv.1110.2365,
title = {Absolute continuity, Lyapunov exponents and rigidity I : geodesic flows},
author = {Artur Avila and Marcelo Viana and Amie Wilkinson},
journal= {arXiv preprint arXiv:1110.2365},
year = {2011}
}
Comments
29 pages. Small error in statement of Theorem A corrected from previous version ("k points" replaced by "k orbits")