arXiv subjects

Matéo Ghezal

Publications and source records attributed to Matéo Ghezal.

2 recordsLinked to original sources

arXiv2025

Finiteness of measures of maximal entropy for smooth saddle surface endomorphisms

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

math.DS↗

arXiv2025

Finitness of measured homoclinic classes with large Lyapunov exponents for $\mathcal{C}^2$ surface diffeomorphisms

We show the finiteness of homoclinic classes carrying measures with large Lyapunov exponents for $\mathcal{C}^2$ surface diffeomorphisms. As a consequence, we derive the finiteness of the set of ergodic measures of maximal entropy, in the case where the entropy of the system is large.

math.DS↗