On Limit Sets of Monotone Maps on Dendroids

被引：1

作者：

Makhrova, E. N. ^{[1
]}

机构：

[1] Lobachevsky State Univ Nizhny Novgorod, Nizhnii Novgorod, Nizhny Novgorod, Russia

来源：

APPLIED MATHEMATICS AND NONLINEAR SCIENCES | 2020年 / 5卷 / 02期

关键词：

dendroid; dendrite; monotone map; periodic point; non-wandering point; omega-limit set; DYNAMICS; DENDRITE;

D O I：

10.2478/AMNS.2020.2.00056

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let X be a dendrite, f : X -> X be a monotone map. In the papers by I. Naghmouchi (2011, 2012) it is shown that omega-limit set omega(x, f) of any point x is an element of X has the next properties: (1) omega(x, f) subset of <(Per(f))over bar>, where Per(f) is the sei of periodic points of f; (2) omega(x, f) is either a periodic orbit or a minimal Cantor set. In the paper by E. Makhrova, K. Vaniukova (2016) it is proved that (3) Omega(F) = <(Per(f))over bar>, where Omega(f) is the set of non-wandering points of f . The aim of this note is to show that the above results (1) - (3) do not hold for monotone maps on dendroids.

引用

页码：311 / 316

页数：6

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