On Ruelle–Perron–Frobenius Operators. II. Convergence Speeds

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...

Spectral theory of transfer operators∗

We give a survey on some recent developments in the spectral theory of transfer operators, also called Ruelle-Perron-Frobenius (RPF) operators, associated to expanding and mixing dynamical systems. Different methods for spectral study are presented. Topics include maximal eigenvalue of RPF operators, smooth invariant measures, ergodic theory for chain of markovian projections, equilibrium state...

Compact weighted Frobenius-Perron operators and their spectra

In this note we characterize the compact weighted Frobenius-Perron operator $p$ on $L^1(Sigma)$ and determine their spectra. We also show that every weakly compact weighted Frobenius-Perron operator on $L^1(Sigma)$ is compact.

Weighted Frobenius-Perron and Koopman operators

Spectrum Properties of the Koopman and Frobenius-Perron Operators