Infinite-dimensional SRB measures

✍ Scribed by J. Bricmont; A. Kupiainen

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 880 KB
• Volume: 103
• Category: Article
• ISSN: 0167-2789
• DOI: 10.1016/s0167-2789(96)00250-3

✦ Synopsis

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.