Discrete potential theory for iterated maps of the interval

Abstract

Using Markov partitions and algebraic graph theory we introduce, in the context of discrete dynamical systems, some laws which characterize the nonlinear dynamics of iterated maps of the interval. In the Markov digraphs we assume that each directed edge has a weight associated to it, given by the Markov invariant measure. This system of weights produces a diffusion process determined by a transition matrix. In this setting, we define a current and a potential which are dynamical invariants.