Random conformal dynamical systems

被引：37
作者：
Deroin, Bertrand [1 ]
Kleptsyn, Victor
机构：
[1] Univ Paris Sud, Dept Math, CNRS, UMR 8628, F-91405 Orsay, France
[2] Univ Geneva, Mat Sect, CH-1211 Geneva 4, Switzerland
[3] Moscow MV Lomonosov State Univ, Independent Univ Moscow, Moscow, Russia
[4] Ecole Normale Super Lyon, CNRS, UMR 5669, UMPA, Lyon, France
来源：
GEOMETRIC AND FUNCTIONAL ANALYSIS | 2007年 / 17卷 / 04期
基金：
俄罗斯基础研究基金会;
关键词：
conformal dynamics; foliation; Brownian motion; harmonic or stationary measure;
D O I：
10.1007/s00039-007-0606-y
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider random dynamical systems such as groups of conformal transformations with a probability measure, or transversally conformal foliations with a Laplace operator along the leaves, in which case we consider the holonomy pseudo-group. We prove that either there exists a measure invariant under all the elements of the group (or the pseudogroup), or almost surely a long composition of maps contracts a ball exponentially. We deduce some results about the unique ergodicity.
引用
收藏
页码：1043 / 1105
页数：63
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