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Displaying similar documents to “Singularities of envelopes of families of submanifolds in ℝ N ”

Catastrophes and partial differential equations

John Guckenheimer (1973)

Annales de l'institut Fourier

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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...

Solutions of Analytical Systems of Partial Differential Equations

Trenčevski, K. (1995)

Serdica Mathematical Journal

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In this paper are examined some classes of linear and non-linear analytical systems of partial differential equations. Compatibility conditions are found and if they are satisfied, the solutions are given as functional series in a neighborhood of a given point (x = 0).

Nodal deformations of singularities.

Jorge A. González-Ramírez (2002)

Revista Matemática Complutense

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In this note we study deformations of a plane curve singularity (C,P) to δ(C,P) nodes. We see that for some types of singularities the method of A'Campo can be carried on using parametric equations. For such singularities we prove that deformations to δ nodes can be made within the space of curves of the same degree.