Spacetime chaos in coupled map lattices

L. A. Bunimovich; Ya G. Sinai

doi:10.1088/0951-7715/1/4/001

Spacetime chaos in coupled map lattices

L. A. Bunimovich, Ya G. Sinai

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233 Scopus citations

Abstract

Coupled map lattices have been introduced for studying systems with spatial complexity. The authors consider simple examples of such systems generated by expanding maps of the unit interval (or circle) with some kind of diffusion coupling. It is shown that such systems have a symbolic representation by two-dimensional lattice models of statistical mechanics. The main result states that the Z² dynamical system generated by space translations and dynamics has a unique invariant mixing Gibbs measure with absolutely continuous finite-dimensional projections. This measure is an analogy of the BRS measure constructed for finite-dimensional hyperbolic transformations.

Original language	English (US)
Article number	001
Pages (from-to)	491-516
Number of pages	26
Journal	Nonlinearity
Volume	1
Issue number	4
DOIs	https://doi.org/10.1088/0951-7715/1/4/001
State	Published - 1988

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy
Applied Mathematics

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abstract = "Coupled map lattices have been introduced for studying systems with spatial complexity. The authors consider simple examples of such systems generated by expanding maps of the unit interval (or circle) with some kind of diffusion coupling. It is shown that such systems have a symbolic representation by two-dimensional lattice models of statistical mechanics. The main result states that the Z2 dynamical system generated by space translations and dynamics has a unique invariant mixing Gibbs measure with absolutely continuous finite-dimensional projections. This measure is an analogy of the BRS measure constructed for finite-dimensional hyperbolic transformations.",

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AU - Sinai, Ya G.

PY - 1988

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AB - Coupled map lattices have been introduced for studying systems with spatial complexity. The authors consider simple examples of such systems generated by expanding maps of the unit interval (or circle) with some kind of diffusion coupling. It is shown that such systems have a symbolic representation by two-dimensional lattice models of statistical mechanics. The main result states that the Z2 dynamical system generated by space translations and dynamics has a unique invariant mixing Gibbs measure with absolutely continuous finite-dimensional projections. This measure is an analogy of the BRS measure constructed for finite-dimensional hyperbolic transformations.

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Spacetime chaos in coupled map lattices

Abstract

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