Spacetime chaos in coupled map lattices

1 November 1988

journal article
Published by IOP Publishing in Nonlinearity

Vol. 1 (4) , 491-516
https://doi.org/10.1088/0951-7715/1/4/001

Abstract

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.

Keywords

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