Complete spectral data for analytic Anosov maps of the torus

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.

19 pages, 4 figures

References in corpus (6)

• The quest for the ultimate anisotropic Banach space
• On the relation between Lyapunov exponents and exponential decay of correlations
• Analytic expanding circle maps with explicit spectra
• Resolvent estimates for operators belonging to exponential classes
• Generic non-trivial resonances for Anosov diffeomorphisms
• Dimension theoretical properties of generalized Baker's transformations

Cited by in corpus (10)

• Dynamic mode decomposition for analytic maps
• Generic non-trivial resonances for Anosov diffeomorphisms
• FBI Transform in Gevrey Classes and Anosov Flows
• An ergodic averaging method to differentiate covariant Lyapunov vectors
• Explicit examples of resonances for Anosov maps of the torus
• Lagrange approximation of transfer operators associated with holomorphic data
• Transfer operator for ultradifferentiable expanding maps of the circle
• Bridging the Gap between Koopmanism and Response Theory: Using Natural Variability to Predict Forced Response
• Locating Ruelle-Pollicott resonances
• Sinai billiard maps with Ruelle resonances