Catastrophes and partial differential equations

John Guckenheimer

Annales de l'institut Fourier (1973)

  • Volume: 23, Issue: 2, page 31-59
  • ISSN: 0373-0956

Abstract

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This paper outlines the manner in which Thom’s theory of catastrophes fits into the Hamilton-Jacobi theory of partial differential equations. The representation of solutions of a first order partial differential equation as lagrangian manifolds allows one to study the local structure of their singularities. The structure of generic singularities is closely related to Thom’s concept of the elementary catastrophe associated to a singularity. Three concepts of the stability of a singularity are discussed.

How to cite

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Guckenheimer, John. "Catastrophes and partial differential equations." Annales de l'institut Fourier 23.2 (1973): 31-59. <http://eudml.org/doc/74128>.

@article{Guckenheimer1973,
abstract = {This paper outlines the manner in which Thom’s theory of catastrophes fits into the Hamilton-Jacobi theory of partial differential equations. The representation of solutions of a first order partial differential equation as lagrangian manifolds allows one to study the local structure of their singularities. The structure of generic singularities is closely related to Thom’s concept of the elementary catastrophe associated to a singularity. Three concepts of the stability of a singularity are discussed.},
author = {Guckenheimer, John},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {2},
pages = {31-59},
publisher = {Association des Annales de l'Institut Fourier},
title = {Catastrophes and partial differential equations},
url = {http://eudml.org/doc/74128},
volume = {23},
year = {1973},
}

TY - JOUR
AU - Guckenheimer, John
TI - Catastrophes and partial differential equations
JO - Annales de l'institut Fourier
PY - 1973
PB - Association des Annales de l'Institut Fourier
VL - 23
IS - 2
SP - 31
EP - 59
AB - This paper outlines the manner in which Thom’s theory of catastrophes fits into the Hamilton-Jacobi theory of partial differential equations. The representation of solutions of a first order partial differential equation as lagrangian manifolds allows one to study the local structure of their singularities. The structure of generic singularities is closely related to Thom’s concept of the elementary catastrophe associated to a singularity. Three concepts of the stability of a singularity are discussed.
LA - eng
UR - http://eudml.org/doc/74128
ER -

References

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  15. [9] R. THOM, Stabilité Structurelle et Morphogenèse, to appear. Zbl0365.92001
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