Chains of infinite order, chains with memory of variable length, and   maps of the interval
  We show how to construct a topological Markov map of the interval whose invariant probability measure is the stationary law of a given stochastic chain of infinite order. In particular we caracterize the maps corresponding to stochastic chains with memory of variable length. The problem treated here is the converse of the classical construction of the Gibbs formalism for Markov expanding maps of the interval. 
Pierre Collet and Antonio Galves
math.PR