 95438 Bricmont J. , Kupiainen A.
 Infinite dimensional SRB measures
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Oct 2, 95

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Abstract. We review the basic steps leading to the construction of a SinaiRuelleBowen (SRB) measure for an infinite lattice of weakly coupled expanding circle maps, and we show that this measure has exponential decay of spacetime correlations. First, using the PerronFrobenius 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 hightemperature phase, and we use a general, but very elementary, method to prove exponential decay of correlations at high temperatures.
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