树映射周期点的存在性定理  

The existence theorem of the periodic point of the tree map

作　　者：郭文旌[1] 胡奇英[1] 

机构地区：[1]西安电子科技大学经济管理学院,陕西西安710071

出　　处：《西安电子科技大学学报》2003年第3期407-409,共3页Journal of Xidian University

基　　金：国家自然科学基金资助项目(70271021)

摘　　要：给定一个闭区间及其上的连续映射,目前的文献已经证明了,如果存在该区间的一个闭子区间满足:它在此区间映射下的象包含其本身,那么这个区间映射一定有不动点.笔者证明了如果一个树映射也满足上述条件,那么这个树映射不一定有不动点,但是它一定有周期点.Given a closed interval and a continuous map on this interval, the current literature proves that if there exists a closed subinterval of this interval that satisfies that its image contains itself, then the interval map must have a fixed point. Does this conclusion hold for tree maps? In this paper, we prove that if a tree map satisfies the above condition, then this tree map may have no fixed point but must have a periodic point.

关 键 词：树映射 周期点 存在性定理 子树 偏序 

分 类 号：O192[理学—数学]