UNSPECIFIED (1993) SPATIOTEMPORAL CHAOS .1. HYPERBOLICITY, STRUCTURAL STABILITY, SPATIOTEMPORAL SHADOWING AND SYMBOLIC DYNAMICS. NONLINEARITY, 6 (2). pp. 165-200. ISSN 0951-7715.

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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 this paper we develop a stable manifold theory for such systems as well as spatio-temporal shadowing, Markov partitions and symbolic dynamics. In the second, we will 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 coupling.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Journal or Publication Title:	NONLINEARITY
Publisher:	IOP PUBLISHING LTD
ISSN:	0951-7715
Official Date:	March 1993
Dates:	Date Event March 1993 UNSPECIFIED
Volume:	6
Number:	2
Number of Pages:	36
Page Range:	pp. 165-200
Publication Status:	Published

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