Explicit examples of resonances for Anosov maps of the torus

Abstract

In [23] Slipantschuk, Bandtlow and Just gave concrete examples of Anosov diffeomorphisms of T 2 for which their resonances could be completely described. Their approach was based on composition operators acting on analytic anisotropic Hilbert spaces. In this note we present a construction of alternative anisotropic Hilbert spaces which helps to simplify parts of their analysis and gives scope for constructing further examples.