English

Finiteness of measures of maximal entropy for smooth saddle surface endomorphisms

Dynamical Systems 2025-11-18 v1

Abstract

We show that C\mathcal{C}^{\infty} 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