FBI transform in Gevrey classes and Anosov flows/ Yannick Guedes Bonthonneau and Malo Jézéquel

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Gevrey microlocal analysis on manifolds -- FBI Transform on compact manifolds -- Ruelle-pollicott resonances and gevrey anosov flows

An analytic FBI transform is built on compact manifolds without boundary, that satisfies all the expected properties. It enables the study of microlocal analytic and Gevrey regularity on such manifolds. This tool is then used to study the Ruelle spectrum of Anosov flows with Gevrey coefficients. In particular, finite order for the associated dynamical determinant is proved.