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SPATIOTEMPORAL CHAOS .1. HYPERBOLICITY, STRUCTURAL STABILITY, SPATIOTEMPORAL SHADOWING AND SYMBOLIC DYNAMICS
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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 | ||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Journal or Publication Title: | NONLINEARITY | ||||
Publisher: | IOP PUBLISHING LTD | ||||
ISSN: | 0951-7715 | ||||
Official Date: | March 1993 | ||||
Dates: |
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Volume: | 6 | ||||
Number: | 2 | ||||
Number of Pages: | 36 | ||||
Page Range: | pp. 165-200 | ||||
Publication Status: | Published |
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