| 关于拓扑强混合及初值敏感依赖 |
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| 引用本文： | 宋晓倩,成丹丹.关于拓扑强混合及初值敏感依赖[J].纺织高校基础科学学报,2008,21(4):435-437. |
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| 作者姓名： | 宋晓倩 成丹丹 |
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| 作者单位： | 西北大学,数学系,陕西,西安,710127 |
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| 基金项目： | 陕西省自然科学基金资助项目
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| 摘 要： | 考虑f为紧致度量空间（X，d）到自身的连续映射，f：K（X）→K（X）为f诱导的集值映射，其中K（X）为X的所有非空紧子集赋予由d诱导的Hausdorff度量所得空间，Ω为K（X）的特殊子空间．研究了f与f^N、f与f^xN以及f与f｜Ω的拓扑强混合、初值敏感依赖之间的关系．
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| 关 键 词： | 拓扑强混合 初值敏感依赖 集值离散动力系统 VIETORIS拓扑 |
On topological strong mixing and sensitive dependence on initial conditions |
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| SOGN Xiao-qian,CHENG Dan-dan.On topological strong mixing and sensitive dependence on initial conditions[J].Basic Sciences Journal of Textile Universities,2008,21(4):435-437. |
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| Authors: | SOGN Xiao-qian CHENG Dan-dan |
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| Affiliation: | SOGN Xiao-qian , CHENG Dan-dan (Department of Mathematics, Northwest University,Xi＇an 710127,China) |
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| Abstract: | It is considered that the continuous map f： X→X and the induced map f： K （X）→K （X）, where X is a compact metric space and K（X） is the space of all non-empty compact subsets of X endowed with the Hausdorff metric H,Ω is a special subspace of K（X）. The relationship between f and f^N,f and f^xN as well as f and f ｜Ω regarding topological strong mixing and sensitive dependence on initial conditions are investigated. |
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| Keywords: | topological strong mixing sensitive dependence on initial conditions set-valued discrete dynamical system Vietoris topology |
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