Coupled map lattices have been introduced for studying systems with spatial complexity. The authors consider simple examples of such systems generated by expanding maps of the unit interval (or circle) with some kind of diffusion coupling. It is shown that such systems have a symbolic representation by two-dimensional lattice models of statistical mechanics. The main result states that the Z2 dynamical system generated by space translations and dynamics has a unique invariant mixing Gibbs measure with absolutely continuous finite-dimensional projections. This measure is an analogy of the BRS measure constructed for finite-dimensional hyperbolic transformations.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics