Modul: MAT760 Ergodic theory and dynamical systems seminar

## A cohomological approach to Ruelle-Pollicott resonances of Anosov diffeomorphisms

Talk by Dr. Daniele Galli

**Date:** 23.10.23 **Time:** 15.00 - 16.00 **Room:** Y27H25

Given a transitive Anosov diffeomorphism on a closed connected manifold, it is known that, for enough smooth observables, the system is mixing w.r.t. the measure of maximal entropy. Accordingly, it makes sense to investigate the speed of decay of correlations and to look for the so-called Ruelle-Pollicott resonances, in order to determine an asymptotic for the correlation limit. In this talk I will describe some recent ideas to tackle these questions. In particular, I will point out some surprising connections between the spectrum of a particular transfer operator acting on suitable Anisotropic Banach spaces of currents and the spectrum of the action induced by the Anosov map on the De Rham cohomology. As a corollary, we obtain an upper bound for the speed of mixing. This talk is based on my PhD thesis that I defended last June at the University of Bologna.''