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

Abstract

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.

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

References in corpus (4)

• Ruelle-Perron-Frobenius spectrum for Anosov maps
• Anisotropic Sobolev spaces and dynamical transfer operators: C^infty foliations
• Kneading determinants and spectra of transfer operators in higher dimensions, the isotropic case
• Banach spaces adapted to Anosov systems

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