Catastrophes and partial differential equations
Annales de l'Institut Fourier, Volume 23 (1973) no. 2, pp. 31-59.

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.

On explore ici le rapport entre la théorie des catastrophes de Thom et la théorie Hamilton-Jacobi des équations différentielles de premier ordre. La représentation des solutions d’une équation aux dérivées partielles du premier ordre comme variétés lagrangiennes permet d’étudier la structure locale de leurs singularités. La structure des singularités génériques est près du concept de Thom de catastrophe élémentaire associée à une singularité. On discute trois notions de la stabilité d’une singularité.

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Guckenheimer, John. Catastrophes and partial differential equations. Annales de l'Institut Fourier, Volume 23 (1973) no. 2, pp. 31-59. doi : 10.5802/aif.455. https://aif.centre-mersenne.org/articles/10.5802/aif.455/

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