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 third session, we introduce Dogopyat's argument, an estimate which excludes high-frequency Ruelle resonances close to the imaginary axis, and thus finishes the proof of the spectral gap for the action of the generator of the flow on an anisotropic distribution space.