Spatio-temporal chaos. III. Natural spatio-temporal measures for coupled circle map lattices

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Abstract
For ptII see ibid., vol.6, p.201 (1993). The authors 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. Their main result is the existence of a natural spatio-temporal measure which is the spatio-temporal analogue of the SRB measure. They developed a stable manifold theory for such systems as well as spatio-temporal shadowing, Markov partitions and symbolic dynamics. They treated in general terms the question of the existence and uniqueness of Gibbs states for the associated higher-dimensional symbolic systems. They study 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 coupling.