Attractors for robust heteroclinic cycles with continua of connections
type: Item
instance of: scholarly article
title: Attractors for robust heteroclinic cycles with continua of connections
zbMATH Open document ID: 0901.58045
published in: Journal of Nonlinear Science
publication date: 1998-11-17T00:00:00Z
review text: The paper studies heteroclinic and homoclinic cycles in continuous dynamical systems with symmetry, with an emphasis on the case when there are multidimensional submanifolds of connecting orbits between fixed points in the cycle. The multidimensionality introduces some new features not present when the sets of connecting orbits are one-dimensional, in particular the cycle need not be topologically closed. Conditions are given to ensure that a homoclinic cycle is asymptotically stable, and that its `principle part' is an attractor in the sense of Milnor.
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 37C80
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 34D45
zbMATH DE Number: 1138722
zbMATH Keywords: homoclinic cycle
zbMATH Keywords: continuous dynamical system
zbMATH Keywords: symmetries
zbMATH Keywords: heteroclinic cycle
Wikidata QID: Q57920981
author: Peter Ashwin
author: Pascal Chossat
reviewed by: Mike Hurley
describes a project that uses: DSTool
MaRDI profile type: Publication
full work available at URL: s003329900045
OpenAlex ID: W1984097539
DOI: 10.1007/S003329900045
description: scientific article; zbMATH DE number 1138722