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The geometry of the elementary catastrophes: (2). The hyperbolic and elliptic umbilics

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

Abstract

This paper presents a description of the geometry of the two three-dimensional singularities which are stable with respect to variation of the families of potentials giving rise to them, though not with respect to perturbation directly of the map. They arise from three dimensional families of potentials with domain or "behavior space" at least two dimensional hence their full geometry is essentially five-dimensional.

Keywords

  • Catastrophe Theory
  • Critical Plane
  • Stable Singularity
  • Behavior Space
  • Cusp Catastrophe

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. Woodcock, A. E. R. & Poston, T., The Geometrical Properties of the Cuspoids (this volume).

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  2. Woodcock, A. E. R. & Poston, T., The Geometrical Properties of the Parabolic Umbilic (this volume).

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  3. Thom, R., Topology, 8 p.313f. 1969.

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  4. Thom, R., Stabilité, Structurelle et Morphogéneśe, published by: Benjamin-Addison Wesley, 1972.

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  5. Zeeman, E. C., In Dynamical Systems, University of Warwick Symposium Volume, published by: Springer-Verlag, 1970.

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© 1974 Springer-Verlag

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Woodcock, A.E.R., Poston, T. (1974). The geometry of the elementary catastrophes: (2). The hyperbolic and elliptic umbilics. In: A Geometrical Study of the Elementary Catastrophes. Lecture Notes in Mathematics, vol 373. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0068969

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  • DOI: https://doi.org/10.1007/BFb0068969

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06681-1

  • Online ISBN: 978-3-540-37941-6

  • eBook Packages: Springer Book Archive