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Abstract

Lyapunov exponents are fundamental invariants in smooth ergodic theory describing the asymptotic, infinitesimal behavior along typical orbits. This text aims to explain how and why to control Lyapunov exponents using entropy for smooth surface diffeomorphisms. We will focus especially on the continuity property of exponents for measures near the maximal entropy measure, by presenting a simplified version of our joint work with S. Crovisier and O. Sarig. Our exposition is intended for advanced students and researchers in dynamics that are not necessarily familiar with smooth ergodic theory.