Generic non-trivial resonances for Anosov diffeomorphisms

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.

19 pages, 1 figure

References in corpus (2)

• Complete spectral data for analytic Anosov maps of the torus
• Analytic expanding circle maps with explicit spectra

Cited by in corpus (5)

• Complete spectral data for analytic Anosov maps of the torus
• FBI Transform in Gevrey Classes and Anosov Flows
• Explicit examples of resonances for Anosov maps of the torus
• Locating Ruelle-Pollicott resonances
• Sinai billiard maps with Ruelle resonances