Complete spectral data for analytic Anosov maps of the torus

TL;DR

This paper constructs a family of analytic hyperbolic diffeomorphisms on the torus and explicitly computes their transfer operator spectra, enabling direct analysis of correlation decay without perturbation methods.

Contribution

It introduces a novel method to explicitly determine the spectral properties of transfer operators for certain Anosov maps on the torus.

Findings

Explicit spectral formulas for transfer operators

Direct computation of correlation decay rates

Analytic hyperbolic diffeomorphisms constructed

Abstract

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