We consider a lattice of weakly coupled expanding circle maps. We construct, via a cluster expansion of the Perron-Frobenius operator, an invariant measure for these innnite dimensional dynamical systems which exhibits space-time-chaos.

We prove that the period doubling operator has an expanding di rection at the xed point We use the induced operator a Perron Frobenius type operator to study the linearization of the period dou bling operator at its xed point We then use a sequence of linear operators with nite ranks to study this induced operator The proof is constructive One can calculate the expanding direction and the rate ...

Finite time coherent sets [Froyland et al., 2010] have recently been defined by a measure-based objective function describing the degree that sets hold together, along with a Frobenius–Perron transfer operator method to produce optimally coherent sets. Here, we present an extension to generalize the concept to hierarchically define relatively coherent sets based on adjusting the finite time coh...

We consider subshifts of nite type on the symbol space generated by incidence matrices over a countably innnite alphabet. We extend the deenition of topological pressure to this context and, as our main result, we construct a new class of Gibbs states of HH older continuous potentials on these symbol spaces. We establish some basic stochastic properties of these Gibbs states: exponential decay ...

A new expansion scheme to evaluate the eigenvalues of the generalized evolution operator (Frobenius-Perron operator) Hq relevant to the fluctuation spectrum and poles of the order-q power spectrum is proposed. The “partition function” is computed in terms of unstable periodic orbits and then used in a finite pole approximation of the continued fraction expansion for the evolution operator. A so...

In this paper, we show a new relation between phase transition in Statistical Mechanics and the dimension of space harmonic functions (SHF) for transfer operator. This is accomplished by extending classical Ruelle-Perron-Frobenius theory to realm low regular potentials defined on either finite or infinite (uncountable) alphabets. We also give an example potential having where Perron-Frobenius e...

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.

The generalized spectral decomposition of the Frobenius-Perron operator of the tent map with varying height is determined at the band-splitting points. The decomposition includes both decay onto the attracting set and the approach to the asymptotically periodic state on the attractor. Explicit compact expressions for the polynomial eigenstates are obtained using algebraic techniques. (c) 1998 A...