Non-Wandering Sets of the Powers of Dendrite Maps

发布时间：2019-04-20 14:09

【摘要】：Let(X, d) be a metric space and f be a continuous map from X to X. Denote by EP(f)and Ω(f) the sets of eventually periodic points and non-wandering points of f, respectively. It is well known that for a tree map f, the following statements hold:(1) If x ∈Ω(f)-Ω(f~n) for some n ≥ 2,then x ∈ EP(f).(2) Ω(f) is contained in the closure of EP(f). The aim of this note is to show that the above results do not hold for maps of dendrites D with Card(End(D)) = ?0(the cardinal number of the set of positive integers).
[Abstract]:Let (X, d) be a metric space and f be a continuous map from X to X. Denote by EP (f) and 惟 (f) the sets of eventually periodic points and non-wandering points of f, respectively. It is well known that for a tree map f, the following statements hold: (1) If x, 惟 (f)-惟 (f 渭 n) for some n 鈮，

本文编号：2461671