每个点都是链回归点的树映射  

TREE MAPS WITH EVERY POINT BEING CHAIN RECURRENT

作　　者：孙太祥[1] 刘新和[1] 徐胜荣 

机构地区：[1]广西大学数学研究所,南宁530004 [2]汕头大学数学研究所,汕头515063

出　　处：《系统科学与数学》2003年第4期566-570,共5页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(10226014);广西科学基金(桂科青0135027)资助课题;广西高校百名中青年学科带头人资助计划项目

摘　　要：设f是端点数为n的树T上的连续自映射且T上的每一点都是f的链回归点.本文证明了: (1)如果T的某个端点是f的不动点,那么,T上的每个点都是f的周期为r≤n-1的周期点,或存在自然数r ≤ n-1,使得fr含有湍流; (2)如果f的不动点都在T的内部,那么,T上的每个点都是f的周期为r≤n的周期点,或存在自然数r≤n,使得,fr含有湍流.Let f be a continuous self-map of a tree T with n end points and every point of T be a chain recurrent point of f. In this paper, we show that: (1) if some end point of T is a fixed point of f, then either every point of T is a periodic point of f with period r < n - 1 or fr has a turbulence for some natural number r < n - 1; (2) if every fixed point of f is a interior point of T, then either every point of T is a periodic point of f with period r < n or fr has a turbulence for some natural number r < n.

关 键 词：链回归点 树映射 周期 湍流 动力学性质 拓扑熵 

分 类 号：O189.11[理学—数学]