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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Numerical detection
of symmetry breaking bifurcation points
with nonlinear degeneracies


Authors: Klaus Böhmer, Willy Govaerts and Vladimí r Janovský
Journal: Math. Comp. 68 (1999), 1097-1108
MSC (1991): Primary 65H10, 58C27, 47H15, 20C30
Published electronically: February 13, 1999
MathSciNet review: 1627846
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Abstract | References | Similar Articles | Additional Information

Abstract: A numerical tool for the detection of degenerated symmetry breaking bifurcation points is presented. The degeneracies are classified and numerically processed on $1$-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.


References [Enhancements On Off] (What's this?)

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Additional Information

Klaus Böhmer
Affiliation: Philipps Universität, Fachbereich Mathematik, Marburg, Germany
Email: boehmer@mathematik.uni-marburg.de

Willy Govaerts
Affiliation: Department of Applied Mathematics and Computer Science, University of Genh, Belgium
Email: Willy.Govaerts@rug.ac.be

Vladimí r Janovský
Affiliation: Faculty of Mathematics and Physics, Charles University, Prague, Czech Republik
Email: janovsky@ms.mff.cuni.cz

DOI: http://dx.doi.org/10.1090/S0025-5718-99-01052-2
PII: S 0025-5718(99)01052-2
Keywords: Symmetry-breaking bifurcation, nonlinear degeneracy, bordered matrices, generalised Liapunov-Schmidt reduction, Newton-like method, pathfollowing
Received by editor(s): February 16, 1996
Received by editor(s) in revised form: August 8, 1997, and December 16, 1997
Published electronically: February 13, 1999
Additional Notes: The first author was partially supported by the Volkswagen Foundation and the Deutsche Forschungsgemeinschaft
The second author was partially supported by the Fund for Scientific Research F.W.O., Gent, Belgium
The third author was partially supported by the grants GAČR 201/98/0528 and GAUK 96/199
Article copyright: © Copyright 1999 American Mathematical Society