Singularities of ray systems. (English) Zbl 0566.58004

Arnol’d, V. I.

Proc. Int. Congr. Math., Warszawa 1983, Vol. 1, 27-49 (1984).

[For the entire collection see Zbl 0553.00001.]
This is a summary of the author’s plenary address to the international congress of mathematicians in Warsaw 1983. It reviews – proofless, but with quite a few examples on hand – recent work (mainly from the last decade) of A. B. Givental’, O. V. Lyashko, O. A. Platatsova, I. G. Shcherbak and others, not to forget the author himself, on the relations between singularities of ray systems and reflection groups, also known as Lagrangian and Legendrian singularity theory in symplectic and in contact geometry. The article is profitably read together with the author’s paper in [Russ. Math. Surv. 38, No. 2, 87–176 (1983); translation from Usp. Mat. Nauk 38, No. 2(230), 77–147 (1983; Zbl 0522.58007)].

Reviewer: H.Crauel

MSC:

58C25	Differentiable maps on manifolds
58K99	Theory of singularities and catastrophe theory
58K35	Catastrophe theory
37J99	Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems

Keywords:

symplectic geometry; caustic; singularities of ray systems; reflection groups; Lagrangian and Legendrian singularity theory; contact geometry

Citations:

Zbl 0553.00001; Zbl 0522.58007