Finiteness of measures of maximal entropy for smooth saddle surface endomorphisms
Dynamical Systems
2025-11-18 v1
Abstract
We show that local diffeomorphisms of closed surfaces whose topological entropy is larger than the logarithm of their degree admit a finite number of ergodic measures of maximal entropy. To do this, we construct families of rectangles, with a nice geometry, displaying a Markov property. We then analyze the behavior of the iterates of unstable curves intersecting these rectangles, using Yomdin theory.
Keywords
Cite
@article{arxiv.2511.12345,
title = {Finiteness of measures of maximal entropy for smooth saddle surface endomorphisms},
author = {Matéo Ghezal},
journal= {arXiv preprint arXiv:2511.12345},
year = {2025}
}
Comments
94 pages,10 figures