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Caustique mystique (d’après Arnold et al.). (Mystic caustics). (French) Zbl 0632.58011

Sémin. Bourbaki, 37e année, Vol. 1984/85, Exp. No. 634, Astérisque 133/134, 19-56 (1986).
[For the entire collection see Zbl 0577.00004.]
This is a survey paper on the generic singularities and their applications in the theory of caustics and the wave fronts. First the author presents some results concerning the Lagrangian and Legendrian foliations on symplectic and contact manifolds. Then he studies the Lagrangian and Legendrian stability of the mappings and the corresponding generic singularities.
A detailed presentation is made of the results obtained by V. I. Arnold and his school concerning the relation between the simple caustics and the discriminants of the Coxeter groups of type \(A_ k\), \(D_ k\), \(E_ k\).
Reviewer: N.Papaghiuc

MSC:

58C25 Differentiable maps on manifolds
58K99 Theory of singularities and catastrophe theory

Citations:

Zbl 0577.00004
Full Text: Numdam EuDML