Strong Positive Recurrence for Diffeomorphisms

Explore a groundbreaking lecture on a new form of hyperbolicity for diffeomorphisms called strong positive recurrence. Delve into the implications of this property, including exponential decay of correlations and Central Limit Theorem for measures maximizing entropy. Discover how strong positive recurrence relates to the continuity of Lyapunov exponents and its application to smooth diffeomorphisms with positive topological entropy on compact surfaces. Learn about this joint work by Jérôme Buzzi, Sylvain Crovisier, and Omri Sarig, presented as part of the Simons Semester on Dynamics.