Sensitivity of dendrite maps

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:446

Article

Shi, Enhui¹  Wang, Suhua²  Di, Yan¹ 

[1] Soochow Univ, Dept Math, Suzhou 215006, Jiangsu, Peoples R China

[2] Jiangsu Univ Sci & Technol, Zhangjiagang Campus, Zhangjiagang 215600, Jiangsu, Peoples R China

关键词: Dendrite;    Sensitivity;    Topological entropy;    Topological transitivity;   

DOI  :  10.1016/j.jmaa.2016.09.020

来源: Elsevier

【 摘 要 】

Suppose that X is a dendrite and f : X -> X is a sensitive continuous map. We show that (a) (X, f) contains a bilaterally transitive subsystem with nonempty interior; (b) the system (X, f) satisfies only one of the following two conditions: (b1) (X, f) contains a topologically transitive subsystem with nonempty interior; (b2) there exists an f-invariant nowhere dense closed subset A of X such that the attraction basin Basin(A, f) contains a residual subset B of an open set and the strong attraction basin Sbasin(A, f) is dense in B; (c) if X is completely regular, then (X, f) contains a relatively strongly mixing subsystem with nonempty interior, dense periodic points and positive topological entropy. Unlike for interval maps, we construct a sensitive dendrite map with zero topological entropy. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free