Zero-Dimensional Principal Extensions

被引：14

作者：

Downarowicz, Tomasz ^{[1
]}

Huczek, Dawid ^{[1
]}

机构：

[1] Wroclaw Univ Technol, Inst Math & Comp Sci, PL-50370 Wroclaw, Poland

来源：

ACTA APPLICANDAE MATHEMATICAE | 2013年 / 126卷 / 01期

关键词：

Topological dynamical system; Principal extension; Zero-dimensional extension;

D O I：

10.1007/s10440-013-9810-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that every topological dynamical system (X,T) has a zero-dimensional principal extension, i.e. a zero-dimensional extension (Y,S) such that for every S-invariant measure nu on Y the conditional entropy h(nu|X) is zero. This reduces the discussion of many entropy-related properties to the zero-dimensional case which gives access to the various useful tools of symbolic dynamics.

引用

页码：117 / 129

页数：13

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