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Numerical detection of symmetry breaking bifurcation points with nonlinear degeneracies |
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| Authors: | Klaus Bö hmer Willy Govaerts Vladimí r Janovský |
| Institution: | Philipps Universität, Fachbereich Mathematik, Marburg, Germany ; Department of Applied Mathematics and Computer Science, University of Genh, Belgium ; Faculty of Mathematics and Physics, Charles University, Prague, Czech Republik |
| Abstract: | A numerical tool for the detection of degenerated symmetry breaking bifurcation points is presented. The degeneracies are classified and numerically processed on  -D restrictions of the bifurcation equation. The test functions that characterise each of the equivalence classes are constructed by means of an equivariant numerical version of the Liapunov-Schmidt reduction. The classification supplies limited qualitative information concerning the imperfect bifurcation diagrams of the detected bifurcation points. |
| Keywords: | Symmetry-breaking bifurcation nonlinear degeneracy bordered matrices generalised Liapunov-Schmidt reduction Newton-like method pathfollowing |
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