Geometry of expanding absolutely continuous invariant measures and the liftability problem
Dynamical Systems
2012-11-07 v3
Abstract
We show that for a large class of maps on manifolds of arbitrary finite dimension, the existence of a Gibbs-Markov-Young structure (with Lebesgue as the reference measure) is a necessary as well as sufficient condition for the existence of an invariant probability measure which is absolutely continuous measure (with respect to Lebesgue) and for which all Lyapunov exponents are positive.
Keywords
Cite
@article{arxiv.0910.2547,
title = {Geometry of expanding absolutely continuous invariant measures and the liftability problem},
author = {Jose F. Alves and Carla L. Dias and Stefano Luzzatto},
journal= {arXiv preprint arXiv:0910.2547},
year = {2012}
}
Comments
21 pages; final version