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

Viviane Baladi

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

Dynamical Systems 2007-05-23 v2

Authors: Viviane Baladi

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.

Keywords

anosov flows anosov representations

Cite

@article{arxiv.math/0408430,
  title  = {Anisotropic Sobolev spaces and dynamical transfer operators: C^infty foliations},
  author = {Viviane Baladi},
  journal= {arXiv preprint arXiv:math/0408430},
  year   = {2007}
}

Comments

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

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