Zero Entropy Systems

被引：20

作者：

Cheng, Wen-Chiao ^{[2
]}

Li, Bing ^{[1
]}

机构：

[1] S China Univ Technol, Dept Math, Guangzhou 510641, Guangdong, Peoples R China

[2] Chinese Culture Univ, Dept Appl Math, Taipei, Taiwan

来源：

JOURNAL OF STATISTICAL PHYSICS | 2010年 / 140卷 / 05期

关键词：

Entropy dimension; Conditional entropy; Dynamical systems; Power rule; Affinity; Symbolic dynamics; LOCAL VARIATIONAL PRINCIPLE; TOPOLOGICAL-ENTROPY; COMPLEXITY; MAPPINGS; SPACES;

D O I：

10.1007/s10955-010-0019-4

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

This paper introduces the notion of entropy dimension to measure the complexity of zero entropy dynamical systems, including the probabilistic and the topological versions. These notions are isomorphism invariants for measure-preserving transformation and continuity. We discuss basic propositions for entropy dimension and construct some examples to show that the topological entropy dimension attains any value between 0 and 1. This paper also gives a symbolic subspace to achieve zero topological entropy, but with full entropy dimension.

引用

页码：1006 / 1021

页数：16

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