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Mat. Sb., 1993, Volume 184, Number 8, Pages 17–36 (Mi msb1003)  

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


Abstract: 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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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1994, 79:2, 347–363

Bibliographic databases:

UDC: 517
MSC: Primary 28D05, 58F11, 58F15; Secondary 60G60, 58F13, 58F10
Received: 01.12.1992

Citation: 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
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\by V.~A.~Volevich
\paper Construction of an~analogue of Bowen--Ruelle--Sinai (measure for a~multidimensional lattice of interacting hyperbolic mappings
\jour Mat. Sb.
\yr 1993
\vol 184
\issue 8
\pages 17--36
\mathnet{http://mi.mathnet.ru/msb1003}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1239757}
\zmath{https://zbmath.org/?q=an:0821.58027}
\transl
\jour Russian Acad. Sci. Sb. Math.
\yr 1994
\vol 79
\issue 2
\pages 347--363
\crossref{https://doi.org/10.1070/SM1994v079n02ABEH003504}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1994PY27400007}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. J. Bricmont, A. Kupiainen, “High temperature expansions and dynamical systems”, Comm Math Phys, 178:3 (1996), 703  crossref  mathscinet  zmath  adsnasa  isi
    2. J. Bricmont, A. Kupiainen, “Infinite-dimensional SRB measures”, Physica D: Nonlinear Phenomena, 103:1-4 (1997), 18  crossref
    3. Leonid A. Bunimovich, “Coupled map lattices: Some topological and ergodic properties”, Physica D: Nonlinear Phenomena, 103:1-4 (1997), 1  crossref
    4. Baladi V., Esposti M., Isola S., Jarvenpaa E., Kupiainen A., “The Spectrum of Weakly Coupled Map Lattices”, J. Math. Pures Appl., 77:6 (1998), 539–584  crossref  mathscinet  zmath  isi
    5. Baladi V., Rugh H., “Floquet Spectrum of Weakly Coupled Map Lattices”, Commun. Math. Phys., 220:3 (2001), 561–582  crossref  mathscinet  zmath  adsnasa  isi
    6. Antônio M. Batista, Ricardo L. Viana, “Kolmogorov–Sinai entropy for locally coupled piecewise linear maps”, Physica A: Statistical Mechanics and its Applications, 308:1-4 (2002), 125  crossref
    7. Jarvenpaa E., “Srb-Measures for Coupled Map Lattices”, Dynamics of Coupled Map Lattices and of Related Spatially Extended Systems, Lecture Notes in Physics, 671, eds. Chazottes J., Fernandez B., Springer-Verlag Berlin, 2005, 95–114  crossref  mathscinet  adsnasa  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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