Distance entropy of dynamical systems on noncompact-phase spaces
文献类型：期刊论文
| 作者 | Dai, Xiongping; Jiang, Yunping |
| 刊名 | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
 |
| 出版日期 | 2008-02-01 |
| 卷号 | 20期号:2页码:313-333 |
| 关键词 | topological entropy Hausdorff dimension pointwise-periodic map |
| ISSN号 | 1078-0947 |
| 英文摘要 | Let X be a separable metric space not necessarily compact, and let f : X -> X be a continuous transformation. From the viewpoint of Hausdorff dimension, the authors improve Bowen's method to introduce a dynamical quantity distance entropy, written as ent(H)(f ; Y), for f restricted on any given subset Y of X; but it is essentially different from Bowen's entropy( 1973). This quantity has some basic properties similar to Hausdorff dimension and is beneficial to estimating Hausdorff dimension of the dynamical system. The authors show that if f is a local lipschitzian map with a lipschitzian constant l then entH(f; Y) <= max{0, HD(Y) log l} for all Y subset of X; if f is locally expanding with skewness. then ent(H)(f; Y) >= HD(Y) log lambda for any Y subset of X. Here HD(-) denotes the Hausdorff dimension. The countable stability of the distance entropy entH proved in this paper, which generalizes the finite stability of Bowen's h-entropy ( 1971), implies that a continuous pointwise periodic map has the distance entropy zero. In addition, the authors show examples which demonstrate that this entropy describes the real complexity for dynamical systems over noncompact-phase space better than that of various other entropies. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000251428100005 |
| 出版者 | AMER INST MATHEMATICAL SCIENCES |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/6940]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Dai, Xiongping |
| 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, Xiongping,Jiang, Yunping. Distance entropy of dynamical systems on noncompact-phase spaces[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,2008,20(2):313-333. |
| APA | Dai, Xiongping,&Jiang, Yunping.(2008).Distance entropy of dynamical systems on noncompact-phase spaces.DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,20(2),313-333. |
| MLA | Dai, Xiongping,et al."Distance entropy of dynamical systems on noncompact-phase spaces".DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS 20.2(2008):313-333. |
入库方式： OAI收割
来源：数学与系统科学研究院
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