Sources, sinks and saddles for expansive homeomorphism with canonical coordinates
type: Item
instance of: scholarly article
title: Sources, sinks and saddles for expansive homeomorphism with canonical coordinates
zbMATH Open document ID: 0638.54032
DOI: 10.1216/RMJ-1987-17-4-673
author: William L. Reddy
author: Lewis C. Robertson
published in: Rocky Mountain Journal of Mathematics
publication date: 1987-01-01T00:00:00Z
review text: Let f be an expansive self-homeomorphism of a compact metric space X and assume that f has canonical coordinates. Since the coordinates change with the movement of a point certain properties of fixed points may be studied for any point. The authors generalize the notions of a source, sink and saddle to any point of X. According to a primary theorem of the paper, if X is compact, connected and locally connected and f is expansive self-homeomorphism of X with canonical coordinates, then X consists of just one point or else every point of X is a saddle point. By means of an example, they show that the condition of local connectedness may not be omitted from the hypotheses.
reviewed by: W. R. Utz
Mathematics Subject Classification ID: 54H20
zbMATH DE Number: 4040817
zbMATH Keywords: expansive self-homeomorphism
zbMATH Keywords: compact metric space
zbMATH Keywords: source
zbMATH Keywords: sink
zbMATH Keywords: saddle
zbMATH Keywords: local connectedness
MaRDI profile type: Publication
full work available at URL: rmj-1987-17-4-673
OpenAlex ID: W2054576681
description: scientific article; zbMATH DE number 4040817