### 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 language | English (US) |
---|---|

Pages (from-to) | 517-546 |

Number of pages | 30 |

Journal | Proceedings of the London Mathematical Society |

Volume | S3-46 |

Issue number | 3 |

DOIs | |

State | Published - 1983 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Proceedings of the London Mathematical Society*,

*S3-46*(3), 517-546. https://doi.org/10.1112/plms/s3-46.3.517

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

Research output: Contribution to journal › Article

*Proceedings of the London Mathematical Society*, vol. S3-46, no. 3, pp. 517-546. https://doi.org/10.1112/plms/s3-46.3.517

}

TY - JOUR

T1 - Classification of Z(2)-equivariant imperfect bifurcations with corank 2

AU - Dangelmayr, G.

AU - Armbruster, Hans

PY - 1983

Y1 - 1983

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0009271127&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0009271127&partnerID=8YFLogxK

U2 - 10.1112/plms/s3-46.3.517

DO - 10.1112/plms/s3-46.3.517

M3 - Article

VL - S3-46

SP - 517

EP - 546

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

SN - 0024-6115

IS - 3

ER -