A cohomological approach to Ruelle-Pollicott resonances and speed of mixing of Anosov diffeomorphisms

Abstract: We investigate Ruelle-Pollicott resonances of Anosov diffeomorphisms with respect to the measure of maximal entropy. We highlight a profound connection between resonances and eigenvalues of the action induced by the dynamics on de Rham cohomology. We finally exploit this relation to get information about the Ruelle-Pollicott asymptotics of the correlation function and establish a cohomological bound for the speed of mixing of Anosov diffeomorphisms.