Continuity Properties of Lyapunov Exponents - Lecture 5

Explore the continuity properties of Lyapunov exponents in this 59-minute lecture by Jérôme Buzzi from Université Paris-Saclay, part of the Simons Semester on Dynamics. Delve into the control of Lyapunov exponents using entropy for smooth surface diffeomorphisms, based on recent joint works with Sylvain Crovisier and Omri Sarig. Learn about computing entropy of measures through the expansion of smooth unstable curves using Yomdin's reparametrization technique. Understand the relationship between potential drops in Lyapunov exponents and "near" homoclinic tangencies, which impede the expansion of unstable curves over extended time periods. Geared towards students and researchers in dynamics, the lecture begins with fundamental concepts in smooth ergodic theory before progressing to main estimates and the proof of the central result. Time permitting, explore consequences such as the spectral gap property for entropy-maximizing measures and the construction of Sinai-Ruelle-Bowen measures.