Measures of maximal entropy for $C^\infty$ three-dimensional flows
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913761152991232 |
|---|---|
| author | Zang, Yuntao |
| author_facet | Zang, Yuntao |
| contents | We prove for $C^\infty$ non-singular flows on three-dimensional compact manifolds with positive entropy, there are at most finitely many ergodic measures of maximal entropy. This result extends the notable work of Buzzi-Crovisier-Sarig (\emph{Ann. of Math.}, 2022) on surface diffeomorphisms. Our approach differs by addressing the continuity of Lyapunov exponents and the uniform largeness of Pesin sets for measures of maximal entropy. Furthermore, it also provides an alternative proof for the case of surface diffeomorphisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21183 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Measures of maximal entropy for $C^\infty$ three-dimensional flows Zang, Yuntao Dynamical Systems We prove for $C^\infty$ non-singular flows on three-dimensional compact manifolds with positive entropy, there are at most finitely many ergodic measures of maximal entropy. This result extends the notable work of Buzzi-Crovisier-Sarig (\emph{Ann. of Math.}, 2022) on surface diffeomorphisms. Our approach differs by addressing the continuity of Lyapunov exponents and the uniform largeness of Pesin sets for measures of maximal entropy. Furthermore, it also provides an alternative proof for the case of surface diffeomorphisms. |
| title | Measures of maximal entropy for $C^\infty$ three-dimensional flows |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2503.21183 |