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arXiv · 1709.04983

$C^1$ density of stable ergodicity

A. Avila·S. Crovisier·A. Wilkinson
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Abstract

We prove a $C^1$ version of a conjecture by Pugh and Shub: among partially hyperbolic volume-preserving $C^r$ diffeomorphisms, $r>1$, the stably ergodic ones are $C^1$-dense. To establish these results, we develop new perturbation tools for the $C^1$ topology: linearization of horseshoes while preserving entropy, and creation of "superblenders" from hyperbolic sets with large entropy.

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A. Avila, S. Crovisier, A. Wilkinson. 2017-09-14. $C^1$ density of stable ergodicity. https://arxiv.org/abs/1709.04983

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