This article is cited in 7 scientific papers (total in 7 papers)
Construction of an analogue of Bowen–Ruelle–Sinai (measure for a multidimensional lattice of interacting hyperbolic mappings
V. A. Volevich
In this paper a dynamical system is studied whose phase space is an infinite product of finite-dimensional manifolds parametrized by the nodes of a multidimensional lattice and whose dynamics consists of a composition of hyperbolic mappings acting independently on each manifold and an interaction which introduces some dependence on adjacent variables. The interaction is assumed to be smooth and one-to-one. For such a dynamical system an invariant measure is constructed, and the system is shown to possess strong mixing properties, both in time and in space relative to this measure; i.e., the phenomenon of spatio-temporal chaos is observed. The idea of the proof is to construct a symbolic dynamics that makes it possible to apply results from the theory of Gibbs random fields.
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Russian Academy of Sciences. Sbornik. Mathematics, 1994, 79:2, 347–363
MSC: Primary 28D05, 58F11, 58F15; Secondary 60G60, 58F13, 58F10
V. A. Volevich, “Construction of an analogue of Bowen–Ruelle–Sinai (measure for a multidimensional lattice of interacting hyperbolic mappings”, Mat. Sb., 184:8 (1993), 17–36; Russian Acad. Sci. Sb. Math., 79:2 (1994), 347–363
Citation in format AMSBIB
\paper Construction of an~analogue of Bowen--Ruelle--Sinai (measure for a~multidimensional lattice of interacting hyperbolic mappings
\jour Mat. Sb.
\jour Russian Acad. Sci. Sb. Math.
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