机构地区: 汕头大学理学院数学研究所
出 处: 《系统科学与数学》 2003年第4期566-570,共5页
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.