树映射的不稳定流形,非游荡集与拓扑熵

Unstable Manifolds, Nonwandering Sets and Topological Entropy of Tree Maps

设f是个端点数为n的树T上的连续自映射.本文得到了f的单侧不稳定流形与拓扑熵的关系,并证明了:（1）如果x∈i=0∞fi（Ω（f））-P（f）,那么,x的轨道是无限的;（2）如果f有一组可循环的不动点,那么h（f）≥In2（n-1）.

Let f be a continuous self-map of tree T with n end point. In this paper, we obtain connection between unilateral unstable manifolds and topological entropy of f and prove that: (1) If x ∈∩i=0∞fi(Ω(f)) -P(f), then the orbit of x is infinite; (2) If f has class of circularible fixed points, then h(f)≥In2/(n-1).