Exact Dynamical Systems and the Frobenius - Perron Operator

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

On Aspects of Numerical Ergodic Theory: Stability of Ulam’s Method, Computing Oseledets Subspaces and Optimal Mixing

A dynamical system is a pairing between a set of states X ⊂ Rd and a map T : X which describes how the system evolves from state to state over time. The Perron– Frobenius, or transfer, operator is a natural extension of the point-by-point dynamics defined by T to an ensemble theory which describes the evolution of distributions of points. It features heavily in dynamical systems theory and in a...

Constrained Frobenius-Perron Operator to Analyse the Dynamics on Composed Attractors*

In this contribution we propose a technique to analyse arbitrary invariant subsets of chaotic dynamical systems. For this purpose we introduce the constrained Frobenius-Perron operator. We demonstrate the use of this operator by determining the geometrical multifractal spectrum of invariant chaotic subsets of one-dimensional maps which are either coexisting side by side indepen­ dently or are e...

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...