| 关于集值离散系统的扩散性 |
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| 引用本文： | 盛业青,顾荣宝.关于集值离散系统的扩散性[J].安徽大学学报(自然科学版),2005,29(3):1-4. |
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| 作者姓名： | 盛业青 顾荣宝 |
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| 作者单位： | 安徽大学,数学与计算科学学院,安徽,合肥,230039;安徽大学,数学与计算科学学院,安徽,合肥,230039 |
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| 基金项目： | 国家自然科学基金;10361001; |
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| 摘 要： | 设(X,d)为度量空间,f:X→X为连续映射,К(X)是X的所有非空紧致子集组成的集族,H是由d诱导的К(X)上的度量,f:К(X)→К(X)定义为f(K)={f(a):a∈K}.本文讨论了f与f的扩散性之间的关系,证明了当f为同胚时,f的扩散性蕴含f的扩散性,并且在К(X)取We拓扑时,二者相互蕴含.
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| 关 键 词： | 超空间 复杂性函数 扩散性 |
| 文章编号： | 1000-2162(2005)03-0001-04 |
| 修稿时间： | 2004年3月6日 |
On scattering property of set -valued discrete systems |
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| SHENG Ye-qing,GU Rong-bao.On scattering property of set -valued discrete systems[J].Journal of Anhui University(Natural Sciences),2005,29(3):1-4. |
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| Authors: | SHENG Ye-qing GU Rong-bao |
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| Abstract: | Let (X,d) be a metric space and f:X→X be a continuous map,К(X) be the class of all nonempty compact subsets of X with the Hausdorff metric H induced by d,define f:К(X)→К(X) as f(K)=｛f(a):a∈K｝. In this note,we investigate the relationships between the scattering property of some set-valued discrete dynamical systems associated to f (collective chaos) and the scattering property of f (individual chaos), show that if f is a homeomorphism,f is scattering implies f is scattering in general and f is scattering if and only if f is scattering when К(X) is endowed with the topology of We. |
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| Keywords: | superspace complexity function scattering property |
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