Modul: MAT760 Ergodic theory and dynamical systems seminar

## Probabilistic limit theorems for the periodic Lorentz gas and for the geodesic flow on a Z^d-cover of a negatively curved compact surface

Talk by Prof. Dr. Françoise Pène

Speaker invited by: Prof. Dr. Corinna Ulcigrai

**Date:** 20.11.23 **Time:** 15.00 - 16.00 **Room:** Y27H25

The two models mentioned in the title are natural examples of dynamical systems preserving an infinite measure. Because of their periodicity, they can be represented by a Z^d-extension over a chaotic probability preserving dynamical system (resp. Sinai billiard, geodesic flow on a compact surface). Thus, their ergodic properties are closely related to those of the underlying probability preserving chaotic system (studied namely by Sinai, Bunimovich, Chernov, Young, Ratner, Pesin, etc.) and in particular with the local limit theorem established by resp. Domokos Szász and Tamás Varjú and Yves Guivarc'h and J. Hardy. When the horizon is finite, the free flight is bounded, and powerful tools can be used to establish many strong results, such as quantitative recurrence results, expansions in mixing, limit theorems for Birkhoff sums, for pin-ball, for non-stationary Birkhoff sums and for solutions of perturbed differential equations (results in collaboration with Benoît Saussol, with Dima Dolgopyat and Péter Nándori, with Damien Thomine, results by Nasab Yassine and Maxence Phalempin). Finally we will also state results in the more difficult case of the Lorentz gas in infinite horizon (results in collaboration with Dalia Terhesiu, and also with Ian Melbourne).''