A Geometrical Study of the Elementary Catastrophes
- PDF / 13,593,084 Bytes
- 262 Pages / 482.4 x 720 pts Page_size
- 6 Downloads / 206 Views
373 A. E. R. Woodcock 1: Poston
A Geometrical Study of the Elementary Catastrophes
Springer-Verlag Berlin Heidelberg NewYork London Paris Tokyo Hong Kong
Authors
A. E. R. Woodcock Department of Biology, Williams College Williamstown, MA01267, USA
T. Poston Department of Mathematics Pohang Institute of Science and Technology P.O. Box 125, Pohang, 680 Korea
1st Edition 1974 3rd Printing 1989
AMS Subject Classifications (1970): 57-02, 57045, 57070, 58F 10 ISBN 3-540-06681-0 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-06681-0 Springer-Verlag New York Berlin Heidelberg
This work is subject to copyright. All rights are reserved, whether the whole or part ofthe material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its version of June 24, 1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law.
© Springer-Verlag Berlin Heidelberg 1974 Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 2141/3140-54321
GENERAL INTRODUCTION
The following papers constitute a study of the precise geometrical nature of the Cuspoid Catastrophes, the Elliptic, Hyperbolic and Parabolic Umbilics and the Reduced Double Cusp.
Stereographic-pair figures permit
a 3-dimensional realization of the Catastrophe Manifolds of the Cuspoid Catastrophes when observed through a stereo viewer.
In introducing these precise pictures into the
literature, it is hoped that they will aid in the application of Catastrophe Theory to the understanding of complex systems such as those of Biology, Physical Chemistry, Economics and Sociology.
Yorktown Heights, New York May 1973
A. E. R. Woodcock
CONTENTS
The Geometry of the Elementary Catastrophes. A. E. R. Woodcock and T. Poston (1) The Cuspoids •••••••••••••••••••••••••••••••• l (2) The Elliptic and Hyperbolic Urnbilics ••••••• 64 (3) The Parabolic Urnbilic •••••••••••••••••••••• 91 Stereographic Reconstructions of the Catastrophe Manifolds of the Cuspoid Catastrophes. A. E. R. Woodcock (1) The Simple Cusp ••••••••••••••••••••••••••• 133 (2) The Swallowtail ••••••••••••••••••••••••••• 149 (3) The Butterfly ••••••••••••••••••••••••••••• 166 (4) The Wigwam •••••••••••••••••••••••••••••••• 193 (5) The Star 212 The Geometrical Properties of the Reduced Double Cusp. A. E. R. Woodcock and T. Poston ••••••••••••••••••••• 232 Acknowledgrnents •••••••••••••••••••••••••••••••• 255 Index
256
THE GEOMETRY OF THE ELEMENTARY CATASTROPHES (1). THE CUSPOIDS
by A. E. R. Woodcock IBM Thomas J. Watson Research Center Yorktown Heights, N.Y. 10598, U.S.A. and T. Poston Instituto de Mathematica Pura e Aplicada Rio-de-Janeiro, Brazil
ABSTRACT:
The Elementary Catastrophes arise as stable singularities
in a system of potentials parameterized by a manifold C (the Co
Data Loading...
