Modul: MAT760 Ergodic Theory and Dynamical Systems Seminar

## Exponential mixing of geodesic flow for geometrically finite manifolds with cusps

Talk by Dr. Jialun Li

**Date:** 30.11.20 **Time:** 15.00 - 16.15 **Room:** Y27H28

Let H^n be the hyperbolic n-space and D be a geometrically finite discrete subgroup in Isom_+(H^n) with cusps. In the joint work with Wenyu Pan, we establish exponential mixing of the geodesic flow over the unit tangent bundle T^1(D \ H^n). Previously, such results were proved by Stoyanov for convex cocompact discrete subgroups and Mohammadi-Oh and Edwards-Oh for D with large critical exponent. We obtain our result by constructing a nice coding for the geodesic flow and then prove a Dolgopyat-like spectral estimate for the corresponding transfer operator. In the talk, I am planning to explain the construction of the coding, which is partly inspired by the works of Lai-Sang Young and Burns-Masur-Matheus-Wilkinson. I will also discuss the application of obtaining a resonance-free region for the resolvent on D\ H^n.