Arnol’d, V. I. Singularities of ray systems. (English) Zbl 0566.58004 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 Cited in 1 ReviewCited in 3 Documents 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 PDF BibTeX XML OpenURL