Remarks on the Existence of Periodic Points for Continuous Maps on Dendrites

被引：0

作者：

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

机构：

[1] Lobachevsky State Univ Nizhny Novgorod, Nizhnii Novgorod 603095, Russia

来源：

LOBACHEVSKII JOURNAL OF MATHEMATICS | 2022年 / 43卷 / 07期

关键词：

dendrite; finite tree; monotone map; continuous map; periodic point; period; minimal set; uniformly recurrent point; DYNAMICS; DEPTH;

D O I：

10.1134/S1995080222100274

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let X be a dendrite, f : X -> X be a continuous map and there exist a subcontinuum Y subset of X such that Y subset of f(Y). In the article we study the conditions of the existence of periodic points of f on Y. We prove the existence of a fixed point on Y, if f is a monotone map. We obtain the conditions on a subcontinuum Y with an uncountable set of end points under which Y has a periodic point. In particular, we obtain the upper estimate for the period of a periodic point on Y, if Y is a finite tree.

引用

页码：1711 / 1719

页数：9

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