### Abstract

Coupled stationary bifurcations in nonlinear operator equations for functions, which are defined on a real interval with non-flux boundary conditions at the ends, are analysed in the framework of imperfect bifurcation theory. The bifurcation equations resulting from a Lyapunov-Schmidt reduction possess a natural structure which can be obtained by taking real parts of a diagonal action in C^{2}of the symmetry group 0(2). A complete unfolding theory is developed and bifurcation equations are classified up to codimension two. Structurally stable bifurcation diagrams are given and their dependence on the wave numbers of the unstable modes is clarified.

Original language | English (US) |
---|---|

Pages (from-to) | 167-192 |

Number of pages | 26 |

Journal | Mathematical Proceedings of the Cambridge Philosophical Society |

Volume | 101 |

Issue number | 1 |

DOIs | |

State | Published - 1987 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Mathematical Proceedings of the Cambridge Philosophical Society*,

*101*(1), 167-192. https://doi.org/10.1017/S0305004100066500

**Coupled stationary bifurcations in non-flux boundary value problems.** / Armbruster, Hans; Dangelmayr, G.

Research output: Contribution to journal › Article

*Mathematical Proceedings of the Cambridge Philosophical Society*, vol. 101, no. 1, pp. 167-192. https://doi.org/10.1017/S0305004100066500

}

TY - JOUR

T1 - Coupled stationary bifurcations in non-flux boundary value problems

AU - Armbruster, Hans

AU - Dangelmayr, G.

PY - 1987

Y1 - 1987

N2 - Coupled stationary bifurcations in nonlinear operator equations for functions, which are defined on a real interval with non-flux boundary conditions at the ends, are analysed in the framework of imperfect bifurcation theory. The bifurcation equations resulting from a Lyapunov-Schmidt reduction possess a natural structure which can be obtained by taking real parts of a diagonal action in C2of the symmetry group 0(2). A complete unfolding theory is developed and bifurcation equations are classified up to codimension two. Structurally stable bifurcation diagrams are given and their dependence on the wave numbers of the unstable modes is clarified.

AB - Coupled stationary bifurcations in nonlinear operator equations for functions, which are defined on a real interval with non-flux boundary conditions at the ends, are analysed in the framework of imperfect bifurcation theory. The bifurcation equations resulting from a Lyapunov-Schmidt reduction possess a natural structure which can be obtained by taking real parts of a diagonal action in C2of the symmetry group 0(2). A complete unfolding theory is developed and bifurcation equations are classified up to codimension two. Structurally stable bifurcation diagrams are given and their dependence on the wave numbers of the unstable modes is clarified.

UR - http://www.scopus.com/inward/record.url?scp=84976074662&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84976074662&partnerID=8YFLogxK

U2 - 10.1017/S0305004100066500

DO - 10.1017/S0305004100066500

M3 - Article

VL - 101

SP - 167

EP - 192

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

SN - 0305-0041

IS - 1

ER -