Different forms of entropy dimension for zero entropy systems

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Title:	Different forms of entropy dimension for zero entropy systems
Authors:	Kuang, Rui Cheng, Wen-Chiao Ma, Dongkui Li, Bing
Contributors:	應數系
Keywords:	topological entropy lower entropy dimension zero entropy systems
Date:	2014-04-03
Issue Date:	2015-01-27 10:40:14 (UTC+8)
Abstract:	The aim of this paper is to introduce the lower s-topological entropy to distinguish zero entropy systems. That this quantity is an invariant factor under topological conjugacy and a power rule is shown. Some examples are given to show that the lower entropy dimension can attain any value in (0, 1), and are different with the upper one and the entropy dimension in the sense of Bowen. A counterexample is used to indicate that the product rule does not hold, and the lower s-topological entropy of the subsystem for the non-wandering set can be strictly less than that of the system when 0 < s < 1. Finally, this study also constructs a dynamical system to show that the transitive system with zero entropy dimension may not be minimal.
Relation:	DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL 卷: 29 期: 2 頁碼: 239-254
Appears in Collections:	[Department of Applied Mathematics] journal articles

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