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Numerical detection of symmetry breaking bifurcation points with nonlinear degeneracies
Author(s):
Klaus
Böhmer;
Willy
Govaerts;
Vladimí r
Janovský.
Journal:
Math. Comp.
68
(1999),
1097-1108.
MSC (1991):
Primary 65H10, 58C27, 47H15, 20C30
Posted:
February 13, 1999
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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.
References:
- 1.
- K. BÖHMER, W. GOVAERTS AND V. JANOVSKÝ, Numerical detection of symmetry breaking bifurcation points with nonlinear degeneracies, Bericht zur Fachbereich Mathematik der Philipps-Universität Marburg 1996.
- 2.
- K. BÖHMER On a numerical Lyapunov-Schmidt method for operator equations, Computing 51, pp. 237-269, 1993. MR 95a:65100
- 3.
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- 5.
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- 6.
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- 7.
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- 8.
- V. JANOVSKÝ AND P. PLECHÁC, Numerical applications of equivariant reduction techniques, in Bifurcation and Symmetry, M. Golubitsky. E. Allgower, K. Böhmer, ed., Birkhäser Verlag, 1992. CMP 94:04
- 9.
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- 10.
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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:
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
Posted:
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 GACR 201/98/0528 and GAUK 96/199
Copyright of article:
Copyright
1999,
American Mathematical Society
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