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 second session, we will define the generator of the flow. Using estimates on the transfer operator, we shall show that the generator is quasi-compact. Finally, we shall prove high-frequency bounds on the resolvent which will be useful for implementing Dolgopyat's argument.