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The geometry of the elementary catastrophes: (3). The Parabolic Umbilic

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Part of the Lecture Notes in Mathematics book series (LNM,volume 373)

Abstract

The Behavior Space of the Parabolic Umbilic is two dimensional and the full geometry of this Umbilic Catastrophe is essentially six-dimensional. This paper describes the geometry of both the non-compact and compact versions of the Parabolic Umbilic.

Keywords

  • Control Space
  • Triangular Region
  • Cusp Point
  • Cusp Region
  • Behavior Space

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This work was begun when both authors were at the Institute of Mathematics, University of Warwick, Coventry CV4 7AL, Warwickshire, England.

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Bibliography

  1. Godwin, N., Three Dimensional Pictures for Thom's Parabolic Umbilic, 1972. I.H.E.S. No. 40, p.117–138.

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  2. Woodcock, A. E. R. & Poston, T., Geometrical Properties of the Reduced Double Cusp (this volume).

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  3. Thom, R., Stabilité Structurelle et Morphogéneśe, Published by Benjamin — Addison Wesley, 1973.

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  4. Zeeman, E. C., Differential Equations for Heartbeat and Nervous Impulse, In: Towards a Theoretical Biology IV ed. by C. H. Waddington.

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© 1974 Springer-Verlag

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Woodcock, A.E.R., Poston, T. (1974). The geometry of the elementary catastrophes: (3). The Parabolic Umbilic. In: A Geometrical Study of the Elementary Catastrophes. Lecture Notes in Mathematics, vol 373. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0068970

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  • DOI: https://doi.org/10.1007/BFb0068970

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06681-1

  • Online ISBN: 978-3-540-37941-6

  • eBook Packages: Springer Book Archive