UNSPECIFIED. (1993) SPATIOTEMPORAL CHAOS .2. UNIQUE GIBBS-STATES FOR HIGHER-DIMENSIONAL SYMBOLIC SYSTEMS. NONLINEARITY, 6 (2). pp. 201-213. ISSN 0951-7715

Abstract

In this series of three papers, we study the geometrical and statistical structure of a class of coupled map lattices with natural couplings. These are infinite-dimensional analogues of Axiom A systems. Our main result is the existence of a natural spatio-temporal measure which is the spatio-temporal analogue of the SRB measure. In the first paper we developed a stable manifold theory for such systems as well as spatio-temporal shadowing, Markov partitions and symbolic dynamics. In this, which is the second, we treat in general terms the question of the existence and uniqueness of Gibbs states for the associated higher-dimensional symbolic systems. The final paper contains the proof of the main theorem which asserts the existence and uniqueness of a natural spatio-temporal measure for certain weakly coupled circle map lattices with a natural couping.

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