A general reduction method for periodic solutions in conservative and reversible systems
type: Item
instance of: scholarly article
title: A general reduction method for periodic solutions in conservative and reversible systems
zbMATH Open document ID: 0855.34044
DOI: 10.1007/BF02218615
author: Jürgen Knobloch
author: A. Vanderbauwhede
published in: Journal of Dynamics and Differential Equations
publication date: 1997-02-03T00:00:00Z
review text: The authors introduce a general method for the study of periodic solutions near equilibria in autonomous systems which are either conservative or reversible. They apply the method of combining normal forms and Lyapunov-Schmidt, which is already introduced for Hamiltonian systems in [the second author and \textit{J.-C. van der Meer}, ``A general reduction method for periodic solutions near equilibria in Hamiltonian systems'', to appear in Normal Forms and Homoclinic Chaos] and for equivariant systems in [the first author, ``Reduction of Hopf bifurcation problem with symmetries'', to appear in Bull. Belg. Math. Soc.] and extends the results of these papers to the cases of conservative and reversible systems.
Mathematics Subject Classification ID: 34C20
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 37G05
zbMATH DE Number: 895795
zbMATH Keywords: periodic solutions
zbMATH Keywords: conservative
zbMATH Keywords: reversible
zbMATH Keywords: normal forms
zbMATH Keywords: Lyapunov-Schmidt
zbMATH Keywords: Hamiltonian systems
reviewed by: Duo Wang
MaRDI profile type: Publication
cites work: Q4849844
cites work: Singularities and groups in bifurcation theory. Volume II
cites work: Reduction of Hopf bifurcation problems with symmetries
cites work: Q4311165
cites work: Q4311169
cites work: Q3326480
description: scientific article; zbMATH DE number 895795