Non-wandering sets of the powers of maps of a star
type: Item
instance of: scholarly article
title: Non-wandering sets of the powers of maps of a star
zbMATH Open document ID: 1028.54037
author: Song Shao
author: Xiangdong Ye
published in: Discrete and Continuous Dynamical Systems
publication date: 2004-01-22T00:00:00Z
review text: Let \(T\) be a star and \(\Omega(f)\) be the set of non-wandering points of a continuous map \(f: T\to T\). For two distinct prime numbers \(p\) and \(q\) the following theorem is proved: (1) \(\Omega(f^p)\cup \Omega(f^q)= \Omega(f)\) for each \(f\in C(T, T)\) if and only if \(pq> \text{End}(T)\), (2) \(\Omega(f^p)\cap \Omega(f^q)= \Omega(f^{pq})\) for each \(f\in C(T, T)\) if and only if \(p+ q\geq \text{End}(T)\), where \(\text{End}(T)\) is the number of the ends of \(T\).
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 37B99
Mathematics Subject Classification ID: 37E25
zbMATH DE Number: 1925727
zbMATH Keywords: star
zbMATH Keywords: non-wandering points
zbMATH Keywords: continuous map
zbMATH Keywords: ends
reviewed by: T. S. Wu
MaRDI profile type: Publication
full work available at URL: dcds.2003.9.1175
OpenAlex ID: W2052031426
DOI: 10.3934/DCDS.2003.9.1175
description: scientific article; zbMATH DE number 1925727