Spectral decomposition of expanding probabilistic dynamical systems

We study probabilistic combinations of expanding dynamical systems, which we call expanding probabilistic dynamical systems, in one dimension. If the system is composed by exact endomorphisms we prove that the probabilistic dynamical system is an exact Markov semigroup, and we determine a generalized spectral decomposition of the associated Markov operator on densities for an example of the tent map coupled with the 2-Renyi map. (C) 1998 Published by Elsevier Science B.V.