Spatio-temporal chaos. I. Hyperbolicity, structural stability, spatio-temporal shadowing and symbolic dynamics
- 1 March 1993
- journal article
- research article
- Published by IOP Publishing in Nonlinearity
- Vol. 6 (2) , 165-200
- https://doi.org/10.1088/0951-7715/6/2/002
Abstract
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 develop a stable manifold theory for such systems as well as spatio-temporal shadowing, Markov partitions and symbolic dynamics. They treat in general terms the question of the existence and uniqueness of Gibbs states for the associated higher-dimensional symbolic systems.Keywords
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