Hausdorff dimensions of zero-entropy sets of dynamical systems with positive entropy

doi:10.1007/s10955-005-7008-z

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	Hausdorff dimensions of zero-entropy sets of dynamical systems with positive entropy
	Dai, XP ; Jiang, YP
	2005-08-01
发表期刊	JOURNAL OF STATISTICAL PHYSICS
ISSN	0022-4715
卷号	120 期号:3-4 页码:511-519
摘要	Suppose that (X, T) is a compact positive entropy dynamical system which we mean that X is a compact metric space and T : X -> X is a continuous transformation of X and the topological entropy h(T) > 0. A point x. X is called a zero-entropy point provided h(T; <(Orb(+)(x)))over bar> = 0, where Orb(+)(x) = {T-n(x) vertical bar n is an element of Z(+)} is the forward orbit of x under T and <(Orb(+)(x))over bar> is the closure. Let epsilon(0) (X, T) denote the set of all zero-entropy points. Naturally, one would like to ask the following important question: How big is epsilon(0)(X, T) for a dynamical system? In this paper, we answer this question. More precisely, we prove that if, furthermore, (X, T) is locally expanding, then the Hausdorff dimension of epsilon(0)(X, T) vanishes.
关键词	zero-entropy point zero-entropy set entropy Hausdorff dimension locally expanding map substitution sequence
DOI	10.1007/s10955-005-7008-z
语种	英语
WOS研究方向	Physics
WOS类目	Physics, Mathematical
WOS记录号	WOS:000232256200003
出版者	SPRINGER/PLENUM PUBLISHERS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/1102
专题	中国科学院数学与系统科学研究院
通讯作者	Dai, XP
作者单位	1.Nanjing Univ, Dept Math, Nanjing 210093, Peoples R China 2.CUNY Queens Coll, Dept Math, Flushing, NY 11367 USA 3.CUNY, Grad Sch, Dept Math, New York, NY 10016 USA 4.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Dai, XP,Jiang, YP. Hausdorff dimensions of zero-entropy sets of dynamical systems with positive entropy[J]. JOURNAL OF STATISTICAL PHYSICS,2005,120(3-4):511-519.
APA	Dai, XP,&Jiang, YP.(2005).Hausdorff dimensions of zero-entropy sets of dynamical systems with positive entropy.JOURNAL OF STATISTICAL PHYSICS,120(3-4),511-519.
MLA	Dai, XP,et al."Hausdorff dimensions of zero-entropy sets of dynamical systems with positive entropy".JOURNAL OF STATISTICAL PHYSICS 120.3-4(2005):511-519.