Thickly Syndetical Sensitivity of Topological Dynamical System
Thickly Syndetical Sensitivity of Topological Dynamical System
复制标题
拓扑动力系统的稠综合敏感性
DOI：
10.1155/2014/583431
复制
发表时间：
2014-01-01
影响因子：
1.4
通讯作者：
Wang, Lidong
中科院分区：
文献类型：
--
作者：
Liu, Heng;Liao, Li;Wang, Lidong
考虑满射连续映射，其中是紧度量空间。本文给出了几种较强的灵敏度，如厚灵敏度、综合灵敏度、厚综合灵敏度和强灵敏度。我们建立如下。(1)如果最小且敏感，则为综合敏感。(2)弱混合意味着较厚的敏感性。(3)如果是最小和弱混合，那么它是厚合成敏感的。(4)如果是一个非极小系统，则它是厚综合敏感的。Devaney混沌意味着厚周期敏感性。(5)给出了一种不厚敏的综合敏感系统。(6)我们给出了厚综合敏感的例子，而不是有限敏感的例子。
Consider the surjective continuous map , where is a compact metric space. In this paper we give several stronger versions of sensitivity, such as thick sensitivity, syndetic sensitivity, thickly syndetic sensitivity, and strong sensitivity. We establish the following. (1) If is minimal and sensitive, then is syndetically sensitive. (2) Weak mixing implies thick sensitivity. (3) If is minimal and weakly mixing, then it is thickly syndetically sensitive. (4) If is a nonminimal -system, then it is thickly syndetically sensitive. Devaney chaos implies thickly periodic sensitivity. (5) We give a syndetically sensitive system which is not thickly sensitive. (6) We give thickly syndetically sensitive examples but not cofinitely sensitive ones.