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Avila, Artur; Crovisier, Sylvain; Wilkinson, Amie (2021). C1 density of stable ergodicity. Advances in Mathematics, 379:107496.
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.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 340 Law
610 Medicine & health 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > General Mathematics |
| Uncontrolled Keywords: | General Mathematics |
| Language: | English |
| Date: | 1 March 2021 |
| Deposited On: | 29 Mar 2021 13:59 |
| Last Modified: | 25 Dec 2024 02:37 |
| Publisher: | Elsevier |
| ISSN: | 0001-8708 |
| OA Status: | Closed |
| Free access at: | Publisher DOI. An embargo period may apply. |
| Publisher DOI: | https://doi.org/10.1016/j.aim.2020.107496 |
Avila, Artur