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.
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页码：18 / 33
页数：16
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