A normally elliptic Hamiltonian bifurcation
type: Item
instance of: scholarly article
title: A normally elliptic Hamiltonian bifurcation
zbMATH Open document ID: 0805.58047
DOI: 10.1007/BF00953660
author: K. Appert
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1993-10-04T00:00:00Z
review text: This work mainly deals with 4-dimensional autonomous Hamiltonian systems in a neighborhood of a degenerate equilibrium, with a double eigenvalue zero (and a purely imaginary pair of eigenvalues). The principal result describes the generic unfoldings of an integrable Hamiltonian, where the parameter space has dimension 3 or 1 depending on whether the linearization is semisimple or not. This uses singularity theory in the planar case. The general non-integrable case is discussed as a perturbation problem, a.o. in the light of a formal reduction to a Hamiltonian normal form.
reviewed by: Dieter Erle
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 37G05
Mathematics Subject Classification ID: 37J40
zbMATH DE Number: 409588
zbMATH Keywords: singularity theory
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: degenerate equilibrium
zbMATH Keywords: unfoldings
zbMATH Keywords: perturbation
zbMATH Keywords: formal reduction
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 409588