| 按序列分布混沌与拓扑混合 |
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| 引用本文： | 杨润生. 按序列分布混沌与拓扑混合[J]. 数学学报, 2002, 45(4): 753-758. DOI: cnki:ISSN:0583-1431.0.2002-04-017 |
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| 作者姓名： | 杨润生 |
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| 作者单位： | 南京师范大学数学与计算机科学学院,江苏,南京,210097 |
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| 基金项目： | 国家自然科学基金资助项目（19871041），江苏省自然科学基金资助项目（BK2001108） |
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| 摘 要： | 本文讨论了按序列分布混沌与拓扑混合的关系,并证明了:若X为至少两点的可分局部紧致度量空间,连续映射f:X→X是拓扑混合的,则对于任一正整数递增序列{mi},存在X的c-稠密Fσ子集D是f按{mi}的某子序列的分布混沌集.
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| 关 键 词： | 分布混沌 拓扑混合 拓扑弱混合 拓扑遍历 |
| 文章编号： | 0583-1431(2002)04-0753-06 |
| 修稿时间： | 2000-07-18 |
Distribution Chaos in a Sequence and Topologically Mixing |
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| Run Sheng YANG. Distribution Chaos in a Sequence and Topologically Mixing[J]. Acta Mathematica Sinica, 2002, 45(4): 753-758. DOI: cnki:ISSN:0583-1431.0.2002-04-017 |
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| Authors: | Run Sheng YANG |
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| Affiliation: | Run Sheng YANG(College of Mathematics and Computer Science, Nanjing Normal University,Nanjing 210097, P. R. China)(E-mail: rshynj@sina.com) |
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| Abstract: | In this paper, we discuss the relation between the distribution chaos and the topologically mixing, show that if a continuous map f : X→X is topologically mixing, where X is a separable locally compact metric space containing at least two points, then for any increasing sequence {mi} of positive integers there exists an c-dense Fσ subset D of X is the set of distribution chaos of f in some sub-sequence of {mi}. |
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| Keywords: | Distribution chaos Topologically mixing Topologically weekly mixing Topologically ergodic |
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