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On Legendre transformations and umbilic catastrophes

Published online by Cambridge University Press:  24 October 2008

M. J. Sewell
M. J. Sewell
Affiliation:
Department of Mathematics, University of Reading
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Extract

In a previous paper this author used elementary mathematics to describe some simple connexions between multi-valued Legendre transformations and those elementary catastrophes having one ‘behaviour’ variable, which belong to a family of polynomials called cuspoids (see Sewell (13)). The Legendre singularities permitted there are isolated and of dimension one, i.e. they exist where a Hessian matrix exceptionally has co-rank one (not more) and elsewhere has full rank (co-rank zero).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 83 , Issue 2 , March 1978 , pp. 273 - 288
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

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