Symmetry restoration in a class of forced oscillators
type: Item
instance of: scholarly article
title: Symmetry restoration in a class of forced oscillators
zbMATH Open document ID: 1034.34050
DOI: 10.1016/S0167-2789(02)00623-1
author: D. Kharzeev
published in: Physica D
publication date: 2002-10-09T00:00:00Z
review text: The author considers families of differential equations \(\dot x=f(x,\lambda,t)\), \(x\in\mathbb{R}^n\). The vector field \(f\) is assumed to be \(T\)-periodic in \(t\). So, in canonical manner, a Poincaré-map \(P\) can be assigned to those systems. Moreover, a particular symmetry is required: \(f(x,\lambda,t)=-f(-x,\lambda,t+(1/2)T)\). Finally, the notion of symmetry restoring bifurcation of \(\omega\)-limit sets of \(P\) has been introduced. The author studies this kind of bifurcation in several examples. The argumentation is based on numerical investigations and the corresponding plots of attractors. In all examples, a collision of a nonsymmetric set and a symmetric set takes place at the critical parameter value. The differences lie in the properties of the limit sets that are involved. Both chaotic and nonchaotic ones are considered. The description of the examples is very short. However, the present paper is based on the PhD thesis of the author where more detailed information can be found.
reviewed by: Jürgen Knobloch
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 1813049
zbMATH Keywords: Forced oscillators
zbMATH Keywords: symmetry restoring bifurcation
describes a project that uses: Dynamics
MaRDI profile type: Publication
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full work available at URL: s0167-2789(02)00623-1
OpenAlex ID: W2004005209
description: scientific article; zbMATH DE number 1813049