In this paper we extend work of Kawamura, see [3], for CuntzKrieger algebras OA for infinite matrices A. We generalize the definition of branching systems, prove their existence for any given matrix A and show how they induce some very concrete representations of OA. We use these representations to describe the Perron-Frobenius operator, associated to an nonsingular transformation, as an infini...

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...

We present in this paper an approach to approximate the Frobenius-Perron transfer operator from a sequence of time-ordered images, that is, a movie dataset. Unlike time-series data, successive images do not provide a direct access to a trajectory of a point in a phase space; more precisely, a pixel in an image plane. Therefore, we reconstruct the velocity field from image sequences based on the...

The wavelet Galerkin operator appears in several different contexts such as wavelets (see for example [Law91b], [Dau95], [CoDa96], [LLS96], [CoRa90]), ergodic theory and g-measures ([Kea82]) or quantum statistical mechanics ([Rue68]). For some of the applications of the Ruelle operator we refer the reader to the book by V. Baladi [Bal00]. It also bears many different names in the literature: th...

We describe the transfer operator approach to coupled map lattices (CML) in cases where the local map is expanding but has no Markov partition (e.g. a general tent map). The coupling is allowed to be non-local, but the total innuence of all sites j 6 = i on site i must be small. The main technical tool are lattice-size independent estimates of Lasota-Yorke type which show that the transfer (Per...

We consider small random perturbations of a large class of nonuniformly hy-perbolic unimodal maps and prove stochastic stability in the strong sense (L 1-convergence of invariant densities) and uniform bounds for the exponential rate of decay of correlations. Our method is based on an analysis of the spectrum of a modiied Perron-Frobenius operator for a tower extension of the Markov chain.