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A buckling model for the set of umbilic catastrophes

Published online by Cambridge University Press:  24 October 2008

J. M. T. Thompson  and
Z. Gaspar
J. M. T. Thompson
Affiliation:
University College London and the Technical University of Budapest
Z. Gaspar
Affiliation:
University College London and the Technical University of Budapest
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Abstract

Zeeman has drawn attention to the sequences in which catastrophes, or modes of instability, can be linked, and it is a common observation that sequences of catastrophes of low order are always found in the environment of catastrophes of higher order. In this paper, a simple buckling model is presented that generates in an elegant manner a complete sequence of the umbilic catastrophes as represented by the semi-symmetric branching points. The scan of a single fundamental parameter of this model is shown to trace a route through all regimes of the umbilic bracelet, giving in turn the hyperbolic, symbolic, elliptic, parabolic and hyperbolic umbilic catastrophes.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 82 , Issue 3 , November 1977 , pp. 497 - 507
Copyright
Copyright © Cambridge Philosophical Society 1977

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