On the centre and the set of ω-limit points of continuous maps on dendrites

被引：13

作者：

Kocan, Zdenek ^{[1
]}

Kornecka-Kurkova, Veronika ^{[1
]}

Malek, Michal ^{[1
]}

机构：

[1] Silesian Univ, Math Inst Opava, Opava 74601, Czech Republic

来源：

TOPOLOGY AND ITS APPLICATIONS | 2009年 / 156卷 / 18期

关键词：

omega-limit set; Recurrent point; Centre of dynamical system; Dendrite; ONE-DIMENSIONAL MAPS; INTERVAL; SPACE;

D O I：

10.1016/j.topol.2009.02.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is well known that for dynamical systems generated by continuous maps of a graph, the centre of the dynamical system is a subset of the set of omega-limit points. In this paper we provide an example of a continuous self-map f(1) of a dendrite such that omega(f(1)) is a proper subset of C(f(1)). The second example is a continuous self-map f(2) of a dendrite having a strictly increasing sequence of omega-limit sets which is not contained in any maximal one. Again, this is impossible for continuous maps on graphs. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：2923 / 2931

页数：9

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