Symplectomorphisms with positive metric entropy
Dynamical Systems
2019-04-03 v1
Abstract
We obtain a dichotomy for -generic symplectomorphisms: either all the Lyapunov exponents of almost every point vanish, or the map is partially hyperbolic and ergodic with respect to volume. This completes a program first put forth by Ricardo Ma\~n\'e. A main ingredient in our proof is a generalization to partially hyperbolic invariant sets of the main result in [Dolgopyat-Wilkinson] that stable accessibility is dense among partially hyperbolic diffeomorphisms.
Cite
@article{arxiv.1904.01045,
title = {Symplectomorphisms with positive metric entropy},
author = {Artur Avila and Sylvain Crovisier and Amie Wilkinson},
journal= {arXiv preprint arXiv:1904.01045},
year = {2019}
}