Diffeomorphisms with positive metric entropy
Dynamical Systems
2017-09-20 v5
Abstract
We obtain a dichotomy for -generic, volume-preserving diffeomorphisms: either all the Lyapunov exponents of almost every point vanish or the volume is ergodic and non-uniformly Anosov (i.e. nonuniformly hyperbolic and the splitting into stable and unstable spaces is dominated). This completes a program first put forth by Ricardo Ma\~n\'e.
Cite
@article{arxiv.1408.4252,
title = {Diffeomorphisms with positive metric entropy},
author = {Artur Avila and Sylvain Crovisier and Amie Wilkinson},
journal= {arXiv preprint arXiv:1408.4252},
year = {2017}
}
Comments
24 pages, 2 figures. The original arXiv submission has been split into two parts, this new version corresponds to the first part. The second part will be available as "$C^1$ density of stable ergodicity", arXiv:1709.04983