Explicit examples of resonances for Anosov maps of the torus

Abstract

In [23], Slipantschuk, Bandtlow and Just gave concrete examples of Anosov diffeomorphisms of the two-torus for which their resonances could be completely described. Their approach was based on composition operators acting on analytic anisotropic Hilbert spaces, and 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.

23 pages, 4 figures

Cited by in corpus (2)

• Bridging the Gap between Koopmanism and Response Theory: Using Natural Variability to Predict Forced Response
• Sharp iteration asymptotics for transfer operators induced by greedy $\beta$-expansions