Quasi-compactness of transfer operators for contact Anosov flows

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Abstract

For any Cr contact Anosov flow with r ≥ 3, we construct a scale of Hilbert spaces, which are embedded in the space of distributions on the phase space and contain all the Cr functions, such that the one-parameter family of transfer operators for the flow extend to them boundedly and that the extensions are quasi-compact. We also give explicit bounds on the essential spectral radii of those extensions in terms of differentiability r and the hyperbolicity exponents of the flow.

Original languageEnglish
Pages (from-to)1495-1545
Number of pages51
JournalNonlinearity
Volume23
Issue number7
DOIs
Publication statusPublished - Jun 28 2010

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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