Infinite-dimensional SRB measures

Bricmont, Jean;Kupiainen, Antti
(1997) Workshop on Lattice Dynamics — Location: UNIV DENIS DIDEROT, PARIS (France) (21.June.1995)

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  • Bricmont, JeanUCLouvain
    Author
  • Kupiainen, AnttiUCLouvain
    Author
Abstract
We review the basic steps leading to the construction of a Sinai-Ruelle-Bowen (SRB) measure for an infinite lattice of weakly coupled expanding circle maps, and we show that this measure has exponential decay of space-time correlations. First, using the Perron-Frobenius operator, one connects the dynamical system of coupled maps on a d-dimensional lattice to an equilibrium statistical mechanical model on a lattice of dimension d + 1. This lattice model is, for weakly coupled maps, in a high-temperature phase, and we use a general, but very elementary, method to prove exponential decay of correlations at high temperatures.
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Bricmont, J., & Kupiainen, A. (1997). Infinite-dimensional SRB measures. Physica D: Nonlinear Phenomena, 103(1-4), 18-33. https://doi.org/10.1016/S0167-2789(96)00250-3 (Original work published 1997)