Classification of Z(2)-equivariant imperfect bifurcations with corank 2

G. Dangelmayr, Hans Armbruster

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

Z(2)-equivariant bifurcation equations in two variables and with a distinguished bifurcation parameter are analysed in the framework of imperfect bifurcation theory in the presence of symmetry. All possible inequivalent bifurcation equations up to codimension 4, together with their universal unfoldings, are collected in a list of normal forms. Conditions are set up which must be satisfied for an arbitrary bifurcation problem to be contact equivalent to a given normal form. The list is supplemented by several normal forms with codimension less than 7 and topological codimension less than or equal to 4.

Original languageEnglish (US)
Pages (from-to)517-546
Number of pages30
JournalProceedings of the London Mathematical Society
VolumeS3-46
Issue number3
DOIs
StatePublished - 1983
Externally publishedYes

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Equivariant
Imperfect
Bifurcation
Normal Form
Codimension
Bifurcation Theory
Less than or equal to
Unfolding
Contact
Symmetry
Arbitrary

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Classification of Z(2)-equivariant imperfect bifurcations with corank 2. / Dangelmayr, G.; Armbruster, Hans.

In: Proceedings of the London Mathematical Society, Vol. S3-46, No. 3, 1983, p. 517-546.

Research output: Contribution to journalArticle

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