Extremes and Self-Recurrence in Dynamical Systems

Explore the intersection of Extreme Value Theory and dynamical systems in this 48-minute lecture from the Workshop on "Rare Events in Dynamical Systems" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the evolution of Extreme Value Theory techniques in dynamical contexts, starting with Collet's 2001 paper on point recurrence in space. Examine the extension to Poisson limit laws, which require asymptotic independence and local recurrence properties. Investigate the concept of self-recurrence of points, addressing the challenges of dependence properties. Learn about recent work extending Collet's average recurrence result to obtain Poisson limit laws with averaged parameters. Gain insights into almost-sure results and their connections to recurrence in a broader context.