完备稠序线性序拓扑空间上的奇周期轨序关系  

The order relation of odd periodic orbits on completely densely ordered linear ordered topological space

作　　者：卢天秀[1,2] 朱培勇[1] 

机构地区：[1]电子科技大学数学科学学院,四川成都610054 [2]四川理工学院理学院,四川自贡643000

出　　处：《纯粹数学与应用数学》2010年第6期915-923,共9页Pure and Applied Mathematics

基　　金：国家自然科学基金(10671134);四川理工学院科研基金(2009XJKYL007)

摘　　要：研究完备稠序线性序拓扑空间上连续自映射的周期轨,指出当连续自映射有(2n+1)-周期轨而没有(2n-1)-周期轨时,该(2n+1)-周期轨上各点的序关系.利用这个关系将Sharkovskii定理从实直线推广到完备稠序线性序拓扑空间上。The periodic orbits of a continuous self-mapping on a completely densely ordered linear ordered topological space is discussed.It pointed out the order relation of the points on the periodic orbit if a continuous self-mapping have a periodic orbit of period（2n＋1） but haven’t periodic orbit of period（2n-1）.By using of this relation,Sharkovskii’s Theorem was extended from real line to completely densely ordered linear ordered topological space.

关 键 词：完备稠序线性序拓扑空间 连续自映射 周期轨 

分 类 号：O189[理学—数学]