Geodesic
Construction of an~analogue of Bowen--Ruelle--Sinai (measure for a~multidimensional lattice of interacting hyperbolic mappings
Sbornik. Mathematics, Tome 79 (1994) no. 2, pp. 347-363

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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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     author = {V. A. Volevich},
     title = {Construction of an~analogue of {Bowen--Ruelle--Sinai} (measure for a~multidimensional lattice of interacting hyperbolic mappings},
     journal = {Sbornik. Mathematics},
     pages = {347--363},
     publisher = {mathdoc},
     volume = {79},
     number = {2},
     year = {1994},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1994_79_2_a6/}
}
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V. A. Volevich. Construction of an~analogue of Bowen--Ruelle--Sinai (measure for a~multidimensional lattice of interacting hyperbolic mappings. Sbornik. Mathematics, Tome 79 (1994) no. 2, pp. 347-363. http://geodesic.mathdoc.fr/item/SM_1994_79_2_a6/