Chaos and order of inverse limit space for a graph map
type: Item
instance of: scholarly article
title: Chaos and order of inverse limit space for a graph map
zbMATH Open document ID: 0984.37042
DOI: 10.1142/S0252959900000042
author: Jie Lü
published in: Chinese Annals of Mathematics. Series B
publication date: 2002-05-01T00:00:00Z
review text: The paper deals with several criteria of chaos for piecewise monotone continuous maps on finite graphs. Here, it is proved that a piecewise monotone continuous map of a finite graph is non-chaotic in the sense of Li-Yorke if and only if the order of the inverse limit space using the map as a sole bonding map. In other words, if the map is non-chaotic, then the topological structure of its inverse limit space is relatively simple, and vice versa. Moreover, he proves that a piecewise monotone continuous map of a finite graph is non-chaotic if and only if every point in the intersection of the set of recurrent points of the map and the closure of the set of periodic points is a regularly recurrent point.
Mathematics Subject Classification ID: 37E25
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 26A18
Mathematics Subject Classification ID: 37B20
zbMATH DE Number: 1445758
zbMATH Keywords: piecewise continuous map chaos
zbMATH Keywords: finite graph
zbMATH Keywords: periodic orbit
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: s0252959900000042
OpenAlex ID: W2523887637
description: scientific article; zbMATH DE number 1445758