Poisson Limit Theorems for Systems with Product Structure

Explore a 34-minute conference talk on Poisson Limit Theorems for systems with product structure, presented by Max Auer at the Workshop on "Rare Events in Dynamical Systems" held at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI). Delve into the speaker's research on obtaining Poisson Limits for return times to small sets in product systems, where only one factor needs to be hyperbolic while the second factor requires only polynomial deviation bounds for ergodic sums. Discover how this approach allows for the inclusion of elliptic or parabolic factors in the second component. Learn about the application of these findings to various maps, including Anosov map X another map combinations, and how they satisfy Poisson Limit Theorems at typical points, with some even satisfying at all points. Gain insights into the potential extension of these methods to certain types of skew products, including T,T-1-maps of high rank.