CONNECTING ERGODICITY AND DIMENSION IN DYNAMIC-SYSTEMS

被引：38

作者：

CUTLER, CD ^{[1
]}

机构：

[1] UNIV WATERLOO,DEPT STAT & ACTUARIAL SCI,WATERLOO N2L 3G1,ONTARIO,CANADA

来源：

ERGODIC THEORY AND DYNAMICAL SYSTEMS | 1990年 / 10卷

关键词：

D O I：

10.1017/S014338570000568X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we make precise the relationship between local or pointwise dimension and the dimension structure of Borel probability measures on metric spaces. Sufficient conditions for exact-dimensionality of the stationary ergodic distributions associated with a dynamical system are obtained. A counterexample is provided to show that ergodicity alone is not sufficient to guarantee exactdimensionality even in the case of continuous maps or flows. © 1990, Cambridge University Press. All rights reserved.

引用

页码：451 / 462

页数：12