| 强一致收敛下的动力性状的遗传性 |
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| 引用本文： | 席凤娟,王延庚.强一致收敛下的动力性状的遗传性[J].西北大学学报,2009,7(1):14-21. |
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| 作者姓名： | 席凤娟 王延庚 |
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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（SJ08A24） |
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| 摘 要： | 为研究连续函数列{fi}的动力性状和极限函数厂的动力性状之间的关系，引入强一致收敛的概念，在函数列{fi}强一致收敛于厂的条件下，证明了函数列{fi}的极小性，拓扑传递性，拓扑弱混合性，拓扑混合性，都可以遗传到f上；并且还得出函数列{fi}的Li-Yorke混沌集（非游荡集）和f的Li-Yorke混沌集（非游荡集）之间的包含关系。最后得出结论：通过对函数列{fi}的动力性状的研究，可以刻画出厂的动力性状。
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| 关 键 词： | 强一致收敛性 极小映射 拓扑传递的 Li-Yorke混沌 非游荡集 拓扑弱混合 拓扑混合 |
The inheritance of dynamical behavior under the condition of strong uniform convergence |
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| XI Feng-juan,WANG Yan-geng.The inheritance of dynamical behavior under the condition of strong uniform convergence[J].Journal of Northwest University(Natural Science Edition),2009,7(1):14-21. |
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| Authors: | XI Feng-juan WANG Yan-geng |
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| Institution: | (Department of Mathmatics, Northwest University, Xi＇an 710127, China) |
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| Abstract: | In order to investigate the relationship between a sequence of continuous functions {fi} and its limit function f on dynamical behavior. Introducing the concept of strong uniform convergence is introduced. The minimality, transitivity, weak mixing, and mixing possessed by {fi} that can be inherited to fare proved, as well as the inclusion relationship between Li-Yorke＇s chaos （non-wandering） set of {fi} andfis gained under the condition of a sequence of continuous functions {fi} strong converges uniformly toil The conclusion is the dynamical behavior of the limit function f can be described through investigating a sequence of continuous functions {fi}. |
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| Keywords: | strong uniform convergence minimal mapping topological transitivity Li-Yorke＇s chaos non-wandering set topological weak mixing topological mixing |
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