Infinite-dimensional SRB measures

被引：32

作者：

Bricmont, J ^{[1
]}

Kupiainen, A ^{[1
]}

机构：

[1] UNIV HELSINKI,DEPT MATH,HELSINKI 00014,FINLAND

来源：

PHYSICA D | 1997年 / 103卷 / 1-4期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1016/S0167-2789(96)00250-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：18 / 33

页数：16

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