On the rate of mixing of circle extensions of Anosov maps

  • Frédéric Naud

    Université d’Avignon, France
On the rate of mixing of circle extensions of Anosov maps cover

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Abstract

Let be an Anosov diffeomorphism. Circle extensions are a rich family of non-uniformly hyperbolic diffeeomorphisms living on for which the rate of mixing is conjectured to be generically exponential. In this paper, using transfer operators on Anisotropic Hilbert spaces, we investigate the possible rates of exponential mixing by exhibiting some explicit lower bounds on the decay rate by spectral techniques. The rates obtained are related to the topological pressure of two times the unstable jacobian.

Cite this article

Frédéric Naud, On the rate of mixing of circle extensions of Anosov maps. J. Spectr. Theory 9 (2019), no. 3, pp. 791–824

DOI 10.4171/JST/263