Dynamics and indecomposable inverse limit spaces of maps on finite graphs
type: Item
instance of: scholarly article
title: Dynamics and indecomposable inverse limit spaces of maps on finite graphs
zbMATH Open document ID: 0792.58027
DOI: 10.1016/0166-8641(93)90016-7
author: Robert P. Roe
published in: Topology and its Applications
publication date: 1993-08-11T00:00:00Z
review text: The author obtains the following results: If the map has a dense orbit on a finite tree then the map is chaotic. Also, if the map on a finite tree has a dense orbit or a homoclinic orbit or periodic points of certain prescribed periods then the associated inverse limit space must contain indecomposable subcontinua. Finally, it is shown that if a map on a finite graph has a set of periodic points of prescribed periods depending on the geometry of the finite graph, then the inverse limit space again must contain an indecomposable subcontinuum.
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 37C25
zbMATH DE Number: 179083
zbMATH Keywords: homoclinic orbit
zbMATH Keywords: periodic points
zbMATH Keywords: inverse limit
MaRDI profile type: Publication
full work available at URL: 0166-8641(93)90016-7
OpenAlex ID: W2018022111
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description: scientific article; zbMATH DE number 179083