强一致收敛下的动力性状的遗传性  

The inheritance of dynamical behavior under the condition of strong uniform convergence

作　　者：席凤娟[1] 王延庚[1] 

机构地区：[1]西北大学数学系,陕西西安710127

出　　处：《西北大学学报（自然科学网络版）》2009年第1期14-21,共8页

基　　金：陕西省自然科学基金资助项目（SJ08A24）

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。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}.

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 

分 类 号：O189.11[理学—数学]