Reversible equivariant Hopf bifurcation
type: Item
instance of: scholarly article
title: Reversible equivariant Hopf bifurcation
zbMATH Open document ID: 1073.34038
author: C. A. Buzzi
author: J. S. W. Lamb
published in: Archive for Rational Mechanics and Analysis
publication date: 2005-03-02T00:00:00Z
review text: This paper is devoted to the study of codimension-one reversible Hopf bifurcation; more precisely, the authors study periodic solutions near an equilibrium whose eigenvalues collide on the imaginary axis, where such a collision arises persistently in a one-parameter family. This situation is also known as 1:1 resonance. In reversible equivariant dynamical systems, there are three types of codimension-one bifurcations of eigenvalues near 1:1 resonance: splitting (from the imaginary axis to the complex plane), passing (on the imaginary axis) and crossing (the imaginary axis). In this paper, the author focus on the case, where Hopf bifurcation takes place with a pair of doubly degenerate eigenvalues on the imaginary axis, with all other eigenvalues nonresonant with respect to the doubly degenrate eigenvalues. This is the simplest context in which reversible equivariant Hopf bifurcation may arise, leading via the Lyapunov-Schmidt reduction to a bifurcation problem in \(\mathbb{R}^{4}\).
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 37G40
Mathematics Subject Classification ID: 37G05
zbMATH DE Number: 2140292
zbMATH Keywords: codimension-one Hopf bifurcation
zbMATH Keywords: reversible equivariant dynamical systems
zbMATH Keywords: Lyapunov-Schmidt reduction
reviewed by: Abdelkader Boucherif
MaRDI profile type: Publication
full work available at URL: s00205-004-0337-2
OpenAlex ID: W2096730707
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DOI: 10.1007/S00205-004-0337-2
description: scientific article; zbMATH DE number 2140292