FBI Transform in Gevrey Classes and Anosov Flows
arXiv:2001.03610
Abstract
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.
v2: Main result improved with respect to v1. Major changes in the presentation v3: Electronic copy of final manuscript accepted for publication
References in corpus (16)
- Ruelle-Perron-Frobenius spectrum for Anosov maps
- Ruelle zeta function at zero for surfaces
- The quest for the ultimate anisotropic Banach space
- Ruelle-Pollicott resonances for real analytic hyperbolic map
- Almost analytic extensions of ultradifferentiable functions with applications to microlocal analysis
- Complete spectral data for analytic Anosov maps of the torus
- Sharp polynomial bounds on the number of Pollicott-Ruelle resonances
- A gentle introduction to anisotropic Banach spaces
- Generic non-trivial resonances for Anosov diffeomorphisms
- A Note on Operator Semigroups Associated to Chaotic Flows
- Analytic hypoellipticity of Keldysh operators
- Fractal Weyl law for the Ruelle spectrum of Anosov flows
- Flow-independent Anisotropic space, and perturbation of resonances
- Viscosity limits for 0th order pseudodifferential operators
- Global trace formula for ultra-differentiable Anosov flows
- An introduction to microlocal complex deformations