圆周上有4周期轨的连续自映射的周期集  

Sets of Periods of Continuous Self-maps with Least Period Four on the Circle

作　　者：顾英[1] 崔菊连[1] 车燕[1] 

机构地区：[1]北京联合大学基础部,北京100101

出　　处：《数学年刊（A辑）》2010年第6期657-666,共10页Chinese Annals of Mathematics

摘　　要：讨论了圆周上有4周期轨的连续自映射的周期集.首先按相对共轭以及相对同伦的关系对圆周上所有有4周期轨的连续自映射分类,再利用映射覆盖图来讨论每一类映射的周期集.最后按同伦最小周期集对圆周上所有有4周期轨的连续自映射进行了分类.将此结果与线段上的Sharkovskii定理对比时可以发现,几乎所有圆周上有4周期轨的连续自映射的周期集都是全体自然数集.This paper deals with the period orbits of continuous self-maps on the circle which have a period orbit with least period 4.The authors classify the continuous self-maps on the circle with finite invariant subset into some homotopy conjugacy classes,and then the set of periods of each class is determined based on the use of f-graph.Finally, a classification of the relative homotopy minimal periods is given.Comparing this result with the Sharkovskii theorem,some differences are pointed out,namely,the minimal set of periods is N for almost all the continuous self-maps on the circle having a period orbit with least period 4.

关 键 词：圆周 周期 Sharkovskii定理 共轭 同伦 

分 类 号：O189.23[理学—数学]