The aim of this manuscript is to understand the dynamics products nonnegative matrices. We extend a well known consequence Perron-Frobenius theorem on periodic points matrix finitely many matrices associated word and later word, possibly infinite length.

In this paper, we attempt to answer the three questions about the invariant probability distribution for stochastic matrices: (1) does every stochastic matrix have an invariant probability distribution?; (2) is the invariant probability distribution unique?; and (3) when can we conclude that the power of a stochastic matrix converges? To answer these questions, we present the Perron-Frobenius T...

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.

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.

Abstract We prove a random Ruelle–Perron–Frobenius theorem and the existence of relative equilibrium states for class open closed interval maps, without imposing transitivity requirements, such as mixing covering conditions, which are prevalent in literature. This provides uniqueness conformal invariant measures with exponential decay correlations, allows us to expand examples (random) dynamica...