Measures of maximal entropy for $C^\infty$ three-dimensional flows
Dynamical Systems
2025-03-28 v1
Abstract
We prove for 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.
Cite
@article{arxiv.2503.21183,
title = {Measures of maximal entropy for $C^\infty$ three-dimensional flows},
author = {Yuntao Zang},
journal= {arXiv preprint arXiv:2503.21183},
year = {2025}
}