Anisotropic Sobolev spaces and dynamical transfer operators: C^infty foliations

Details Anisotropic Sobolev spaces and dynamical transfer operators: C^infty foliations Anisotropic Sobolev spaces and dynamical transfer operators: C^infty foliations

2004-08-31

arxiv.org/abs/math/0408430v2

Mathematics

Dynamical Systems

Revised version. Technical points clarified. Statements for t=1 or infty suppressed

Scientific paper

We consider a smooth Anosov diffeomorphism with a smooth dynamical foliation. We show upper bounds on the essential spectral radius of its transfer operator acting on anisotropic Sobolev spaces. (Such bounds are related to the essential decorrelation rate for the SRB measure.) We compare our results to the estimates of Kitaev on the domain of holomorphy of dynamical Fredholm determinants for differentiable dynamics.

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