Ruelle-perron-frobenius Spectrum for Anosov Maps

Finite Approximation of Sinai-Bowen-Ruelle Measures for Anosov Systems in Two Dimensions

We describe a computational method of approximating the \physical" or Sinai-Bowen-Ruelle measure of an Anosov system in two dimensions. The approximation may either be viewed as a xed point of an approximate Perron-Frobenius operator or as an invariant measure of a randomly perturbed system.

Fredholm Determinants, Anosov Maps and Ruelle Resonances

I show that the dynamical determinant, associated to an Anosov diffeomorphism, is the Fredholm determinant of the corresponding RuellePerron-Frobenius transfer operator acting on appropriate Banach spaces. As a consequence it follows, for example, that the zeroes of the dynamical determinant describe the eigenvalues of the transfer operator and the Ruelle resonances and that, for C∞ Anosov diff...

Spectrum Properties of the Koopman and Frobenius-Perron Operators

On Ruelle–Perron–Frobenius Operators. I. Ruelle Theorem

We study Ruelle–Perron–Frobenius operators for locally expanding and mixing dynamical systems on general compact metric spaces associated with potentials satisfying the Dini condition. In this paper, we give a proof of the Ruelle Theorem on Gibbs measures. It is the first part of our research on the subject. The rate of convergence of powers of the operator will be presented in a forthcoming pa...

Kms States on C*-algebras Associated to Expansive Maps

Using Walters’ version of the Ruelle-Perron-Frobenius Theorem we show the existence and uniqueness of KMS states for a certain one-parameter group of automorphisms on a C*-algebra associated to a positively expansive map on a compact metric space.