Iterated function systems and dynamical systems

We study the relationship between measures invariant for a piecewise expanding transformation tau of a compact metric space endowed with a underlying measure and measures invariant for an iterated function system T(tau), generated by inverse branches of tau. The main result says that the tau-invariant absolutely continuous measure &mgr; is also T(tau) invariant if and only if tau is absolutely continuously conjugated with a piecewise linear transformation. Measures of maximal entropy and general equilibrium states are also discussed. (c) 1995 American Institute of Physics.