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The geometrical properties of the Reduced Double Cusp

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

Abstract

The Bifurcation Sets of the Reduced Double Cusp V=A(x4+y4−6x2y2)+B(x3−3xy2)+C (x2+y2) -ux-vy were drawn to investigate the possibility of the existence of three-, four- and five-fold symmetry in the projected envelope. While three-and four-fold symmetry could be demonstrated, it was impossible to demonstrate five-fold symmetry. However, modifying one of the parametic equations in a heuristic way did permit the production of a figure with five-fold symmetry.

Keywords

  • Singular Point
  • Geometrical Property
  • Critical Curve
  • Control Space
  • Critical Curf

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. Thom, R., In: American Mathematical Society, Lectures on Mathematics in the Life Sciences, Ed. by J. Cowan, Providence, Rhode Island, 1972.

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  2. Woodcock, A. E. R. and Poston, T., The Geometrical Properties of the Elementary Catastrophes, The Cuspoids, (this volume).

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  3. Woodcock, A. E. R. and Poston, T., The Geometrical Properties of the Elementary Catastrophes (2) The Elliptic and Hyperbolic Umbilics (this volume).

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  4. Woodcock, A. E. R. and Poston, T., The Geometrical Properties of the Elementary Catastrophes (3) The Parabolic Umbilic (this volume).

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  5. Woodcock, A. E. R. and Poston, T., On the Geometry of Certain Potential Functions with Two-Fold Symmetry. (To appear)

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  6. Woodcock, A. E. R., Poston, T. and Stewart, I.N., The Full Unfolding of the Double Cusp (to appear).

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© 1974 Springer-Verlag

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Woodcock, A.E.R., Poston, T. (1974). The geometrical properties of the Reduced Double Cusp. In: A Geometrical Study of the Elementary Catastrophes. Lecture Notes in Mathematics, vol 373. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0068976

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  • DOI: https://doi.org/10.1007/BFb0068976

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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