Contact Anosov flows and the FBI transform

Abstract

This paper is about spectral properties of transfer operators for contact Anosov flows. The main result gives the essential spectral radius of the transfer operators acting on the so-called anisotropic Sobolev space exactly in terms of dynamical exponents. Also we provide a simplified proof by using the FBI transform.

34 pages, no figures; Corrected typos, changed notation slightly, added a few remarks