局部紧致动力系统中几乎周期点的存在性  

The existence of almost periodic points in locally compact dynamical systems

作　　者：陈苁[1] 

机构地区：[1]西北大学数学系,陕西西安710127

出　　处：《纺织高校基础科学学报》2010年第2期141-143,共3页Basic Sciences Journal of Textile Universities

基　　金：陕西省自然科学基金资助项目(SJ08A24)

摘　　要：讨论底空间为局部紧致的第二可数Hausdorff空间动力系统中几乎周期点的存在性问题.利用映射f的扩充,紧致动力系统中一定存在几乎周期点,讨论底空间为局部紧致空间时各种情况下的几乎周期点存在的条件.给出各种情形下几乎周期点存在与否的条件.当底空间为更一般的局部紧致空间时,动力系统中几乎周期点存在条件比底空间为紧致空间时动力系统中几乎周期点存在条件更复杂.The existence of almost periodic points for dynamical systems on the second countable locally compact Hausdorff space is investigated.By using of the expansion of f,there exist almost periodic points in compact dynamical systems,a classification of conditions for almost periodic points is established for the dynamical systems on second countable locally compact Hausdorff space.The existence conditions of almost periodic points under every situation are given in locally compact dynamical systems.The existence conditions of almost periodic points are more complex in locally compact dynamical systems than in compact dynamical systems.

关 键 词：连续映射 紧致动力系统 局部紧致动力系统 几乎周期点 子系统 扩充 

分 类 号：O189.1[理学—数学]