$C^1$ density of stable ergodicity
Dynamical Systems
2017-09-18 v1
Abstract
We prove a version of a conjecture by Pugh and Shub: among partially hyperbolic volume-preserving diffeomorphisms, , the stably ergodic ones are -dense. To establish these results, we develop new perturbation tools for the topology: linearization of horseshoes while preserving entropy, and creation of "superblenders" from hyperbolic sets with large entropy.
Cite
@article{arxiv.1709.04983,
title = {$C^1$ density of stable ergodicity},
author = {A. Avila and S. Crovisier and A. Wilkinson},
journal= {arXiv preprint arXiv:1709.04983},
year = {2017}
}
Comments
58 pages, 11 figures. The long version of "Diffeomorphisms with positive metric entropy" arXiv:1408.4252v3 has been split in two, and this paper corresponds to the second part. The first part is available as the current version of arXiv:1408.4252