# On entropy and volume growth

 Orateur: Yuntao ZANG Localisation: Université Paris 11, France Type: Séminaire COOL Site: Hors LAMA , IHP Salle: Salle 05 Date de début: 04/10/2019 - 10:00 Date de fin: 04/10/2019 - 11:00

Let $f$ be a $C^{1+\alpha}$ diffeomorphism on a compact manifold $M$ and let $\mu$ be an ergodic measure. We prove that the metric entropy of $\mu$ is bounded from above by a mixture between the sum of the positive Lyapunov exponents and the volume growth (or topological entropy) on some sub-manifold.