Arnol’d, V. I.; Varchenko, A. N.; Givental’, A. B.; Khovanskij, A. G. Singularities of functions, wave fronts, caustics and multidimensional integrals. (English) Zbl 0546.58007 Sov. Sci. Rev., Sect. C, Math. Phys. Rev. 4, 1-92 (1984). This is a survey of the authors’ results about the theory of singularities which have appeared elsewhere. In Section 1 they discuss the classification theory of singularities of systems of rays and fronts in geometrical optics. In Section 2 they use the result in Section 1 for studying shortwave asymptotics in the neighbourhood of singularities of caustics. They also give formulas for calculating asymptotics of integrals by using Newton’s polyhedra of singularities. These results can be found in the book by the first author, S. M. Gusein-Zade and the second author [Singularities of differentiable maps, Vol. I (1985)]. Reviewer: S.Izumiya Cited in 1 ReviewCited in 1 Document MSC: 58C25 Differentiable maps on manifolds 58K99 Theory of singularities and catastrophe theory 78A05 Geometric optics Keywords:singularities of systems of rays; geometrical optics; caustics; Newton’s polyhedra PDFBibTeX XMLCite \textit{V. I. Arnol'd} et al., Sov. Sci. Rev., Sect. C 4, 1--92 (1984; Zbl 0546.58007)