Nonwandering points of monotone local dendrite maps revisited

被引：6

作者：

Abdelli, Hafedh ^{[1
,3
]}

Abouda, Haithem ^{[2
]}

Marzougui, Habib ^{[3
]}

机构：

[1] Univ Monastir, Univ Carthage, Fac Sci Bizerte, UR17ES21,Dynam Syst & Their Applicat,Monastir Pre, Monastir, Tunisia

[2] Univ Carthage, Fac Sci Bizerte, Jarzouna 7021, Tunisia

[3] Univ Carthage, Fac Sci Bizerte, UR17ES21, Dynam Syst & Applicat, Jarzouna 7021, Tunisia

来源：

TOPOLOGY AND ITS APPLICATIONS | 2018年 / 250卷

关键词：

Nonwandering; Local dendrite; Graph; Dendrite; Monotone map; NON-WANDERING SETS; OMEGA-LIMIT SETS; POWERS;

D O I：

10.1016/j.topol.2018.10.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let X be a local dendrite and let f : X -> X be a monotone map. Denote by P(f) and Omega(f) the sets of periodic points and nonwandering points of f, respectively. We show that Omega(f) = <(P(f))over bar>, whenever P(f) is nonempty and Omega(f) is the unique minimal set included in a circle which is either a Cantor set or a circle, whenever P(f) is empty. In the case where the set of endpoints of X is countable, we show that Omega(f) = P(f) whenever P(f) is nonempty. (C) 2018 Published by Elsevier B.V.

引用

页码：61 / 73

页数：13

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