In this reading group, we study the article "On contact Anosov flows" written by C.Liverani. Its goal is to show exponential decay of correlations for contact Anosov flows by studying their Ruelle resonances.

In this first session, we will start by introducing Anisotropic Banach spaces tailored for this study. We then explain how to make sense of the transfer operator on those spaces and conclude by showing a Lasota-Yorke inequality that controls its essential spectrum.