Paper

Generic non-trivial resonances for Anosov diffeomorphisms

Published 7 February 2017 • © 2017 IOP Publishing Ltd & London Mathematical Society
, , Citation Alexander Adam 2017 Nonlinearity 30 1146 DOI 10.1088/1361-6544/aa59a9

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alexander.adam@imj-prg.fr

Author affiliations

1 Sorbonne Universités, UPMC Univ. Paris 6, CNRS, Institut de Mathématiques de Jussieu, 4, Place Jussieu, 75005 Paris, France

Dates

  1. Received 26 May 2016
  2. Accepted 16 January 2017
  3. Published

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0951-7715/30/3/1146

Abstract

We study real analytic perturbations of hyperbolic linear automorphisms on the 2-torus. The Koopman and the transfer operator are nuclear of order 0 when acting on a suitable Hilbert space. We show the generic existence of non-trivial Ruelle resonances for both operators. We prove that some of the perturbations preserve the volume and some of them do not.

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10.1088/1361-6544/aa59a9