Topological fixed point theorems do not hold for random dynamical systems

被引：0

作者：

Ochs G. ^{[1
]}

Oseledets V.I. ^{[2
]}

机构：

[1] Institut für Dynamische Systeme, Universität Bremen, 28334 Bremen

[2] Department of Mechanics and Mathematics, Moscow State University

来源：

Journal of Dynamics and Differential Equations | 1999年 / 11卷 / 4期

关键词：

Cocyele; Fixed point theorem; Invariant measure; Random dynamical system;

D O I：

10.1023/A:1022670227876

中图分类号：

学科分类号：

摘要：

The aim of this paper is to demonstrate that topological fixed point theorems have no canonical generalization to the case of random dynamical systems. This is done by using tools from algebraic ergodic theory. We give a criterion for the existence of invariant probability measures for group valued cocyeles. With that, examples of continuous random dynamical systems on a compact interval without random invariant points, which are an appropriate generali/ation of fixed points, are constructed. © 1999 Plenum Publishing Corporation.

引用

页码：583 / 593

页数：10

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