Hausdorff dimensions of zero-entropy sets of dynamical systems with positive entropy
文献类型：期刊论文
| 作者 | Dai, XP; Jiang, YP |
| 刊名 | JOURNAL OF STATISTICAL PHYSICS
 |
| 出版日期 | 2005-08-01 |
| 卷号 | 120期号:3-4页码:511-519 |
| 关键词 | zero-entropy point zero-entropy set entropy Hausdorff dimension locally expanding map substitution sequence |
| ISSN号 | 0022-4715 |
| DOI | 10.1007/s10955-005-7008-z |
| 英文摘要 | 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. |
| WOS研究方向 | Physics |
| 语种 | 英语 |
| WOS记录号 | WOS:000232256200003 |
| 出版者 | SPRINGER/PLENUM PUBLISHERS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/1101]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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