FBI Transform in Gevrey Classes and Anosov Flows

This monograph has a triple purpose. The first chapter is dedicated to the study of semi-classical pseudo-differential operators whose symbols are Gevrey in all variables. In the second one, the theory of I-lagrangian functional spaces is presented, in the case that the lagrangian is not a compactly supported deformation of the cotangent. The relation with the operators presented before is also analyzed. In the last chapter, the theory is applied to the study of Gevrey Anosov flows: in particular, the growth of their dynamical determinants is investigated.