The centre and the depth of the centre for continuous maps on dendrites with unique branch point
The centre and the depth of the centre for continuous maps on dendrites with unique branch point
复制标题
具有唯一分支点的树突上连续映射的中心和中心深度
DOI：
10.1016/j.topol.2020.107314
复制
发表时间：
2020
影响因子：
0.6
通讯作者：
Xia G
中科院分区：
文献类型：
--
作者：
Su G;Sun T;Li L;Han C;Xia G
设D是具有唯一分支点的树枝晶，f：D→D是连续的。用R(F)和Ω(F)分别表示f的回归点和非游荡点的集合。对任意正整数k，设Ω0(F)=D，Ωk(F)=Ω(f|Ωk−1(F))，满足Ωk(F)=Ωk+1(F)的极小k称为f的深度，其中k为正整数或∞。本文证明了Ω2(F)=R(F)‾且f的深度至多为2。
Let D be a dendrite with unique branch point and f: D→ D be continuous. Denote by R (f) and Ω (f) the set of recurrent points and the set of non-wandering points of f, respectively. Let Ω 0 (f)= D and Ω k (f)= Ω (f| Ω k− 1 (f)) for any positive integer k. The minimal k such that Ω k (f)= Ω k+ 1 (f) is called the depth of f, where k is a positive integer or∞. In this note, we show that Ω 2 (f)= R (f)‾ and the depth of f is at most 2.