Accumulation points of flows on the Klein bottle
type: Item
instance of: scholarly article
title: Accumulation points of flows on the Klein bottle
zbMATH Open document ID: 1029.37025
author: Gabriel Soler López
published in: Discrete and Continuous Dynamical Systems
publication date: 2003-07-15T00:00:00Z
review text: The paper characterizes the sets that can occur as omega-limit sets of smooth flows on the Klein bottle \(K\), by defining a notion of admissible set and showing that any omega-limit set is the boundary of an admissible set, and conversely, given an admissible set \(S\subset K\) there is a smooth flow on \(K\) and a point \(x\) of \(S\) such that the omega-limit set of \(x\) is the boundary of \(S\). \(S\subset K\) is admissible provided that it is a proper, connected, open subset whose complement is connected, and with the property that for any non null homotopic Jordan curve \(\beta\) in \(S\), \ there is a component \(C\) of \(S - \beta\) such that the boundary of \(C\) contains that of \(S\).
Mathematics Subject Classification ID: 37E35
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 34E99
zbMATH DE Number: 1890751
zbMATH Keywords: omega-limit sets
zbMATH Keywords: Klein bottle
zbMATH Keywords: admissible set
zbMATH Keywords: smooth flow
reviewed by: Mike Hurley
MaRDI profile type: Publication
full work available at URL: dcds.2003.9.497
OpenAlex ID: W2024819129
DOI: 10.3934/DCDS.2003.9.497
description: scientific article; zbMATH DE number 1890751