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A note on non-degenerate umbilics and the path formulation for bifurcation problems

Published online by Cambridge University Press:  12 July 2007

Jacques-Elie Furter  and
Angela Maria Sitta
Jacques-Elie Furter
Affiliation:
Department of Mathematical Sciences, Brunel University, Uxbridge UB8 3PH, UK (mastjef@brunel.ac.uk)
Angela Maria Sitta
Affiliation:
Departamento de Matemática, IBILCE–UNESP, Brazil (angela@mat.ibilce.unesp.br)
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Abstract

Path formulation can be used to classify and structure efficiently multiparameter bifurcation problems around fundamental singularities: the cores. The non-degenerate umbilic singularities are the generic cores for four situations in corank 2: the general or gradient problems and the Z2-equivariant (general or gradient) problems. Those categories determine an interesting ‘Russian doll’ type of structure in the universal unfoldings of the umbilic singularities.

One advantage of our approach is that we can handle one, two or more parameters using the same framework (even considering some special parameter structure, for instance, some internal hierarchy). We classify the generic bifurcations that occur in those cases with one or two parameters.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 134 , Issue 6 , December 2004 , pp. 1115 - 1126
Copyright
Copyright © Royal Society of Edinburgh 2004

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