KINETICS OF COUPLED MAP LATTICES

A simple example of coupled map lattices generated by expanding maps of the unit interval with some kind of diffusion coupling is considered. It has been stated that this system has an unique invariant mixing measure with absolutely continuous finite-dimensional projections. Here we prove that probability measures from some natural class weakly converge to this measure under the actions of dynamics. The main idea of the proof is the symbolic representation of our system by two-dimensional lattice model of statistical mechanics. It provides the possibility of applying results from random field theory.