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Anisotropic Sobolev spaces and dynamical transfer operators: \(C^\infty\) foliations. (English) Zbl 1158.37304
Kolyada, S. (ed.) et al., Algebraic and topological dynamics. Proceedings of the conference, Bonn, Germany, May 1–July 31, 2004. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3751-6/pbk). Contemporary Mathematics 385, 123-135 (2005).
Summary: 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.
For the entire collection see [Zbl 1075.37001].

MSC:
37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
37C30 Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc.
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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