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Complete spectral data for analytic Anosov maps of the torus

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Published 23 May 2017 • © 2017 IOP Publishing Ltd & London Mathematical Society
, , Citation J Slipantschuk et al 2017 Nonlinearity 30 2667 DOI 10.1088/1361-6544/aa700f

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Author e-mails

J.Slipantschuk@qmul.ac.uk

O.Bandtlow@qmul.ac.uk

W.Just@qmul.ac.uk

Author affiliations

1 School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom

Author notes

2 Author to whom any correspondence should be addressed.

Dates

  1. Received 9 May 2016
  2. Accepted 28 April 2017
  3. Published

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0951-7715/30/7/2667

Abstract

Using analytic properties of Blaschke factors we construct a family of analytic hyperbolic diffeomorphisms of the torus for which the spectra of the associated transfer operator acting on a suitable Hilbert space can be computed explicitly. As a result, we obtain expressions for the decay of correlations of analytic observables without resorting to any kind of perturbation argument.

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10.1088/1361-6544/aa700f