120329630
Weak asymptotics for the numbers of solutions of diophantine problems
117668456
Singularities, bifurcations, and catastrophes
The first information on catastrophe theory appeared in the western press in the late sixties. In magazines like “News-week” there were reports of a revolution in mathematics, comparable perhaps to Newton’s invention of the differential and integral calculus. It was claimed that the new science, catastrophe theory, was much more valuable to mankind than mathematical analysis: while Newtonian theory only considers smooth, continuous processes, catastrophe theory provides a universal method for the study of all jump transitions, discontinuities, and sudden qualitative changes. There appeared hundreds of scientific and popular science publications in which catastrophe theory was applied to such diverse targets as, for instance, the study of heart beat, geometrical and physical optics, embryology, linguistics, experimental psychology, economics, hydrodynamics, geology, and the theory of elementary particles. Among the published works on catastrophe theory are studies of the stability of ships, models for the activity of the brain and mental disorders, for prison uprisings, for the behaviour of investors on the stock exchange, for the influence of alcohol on drivers and for censorship policy with respect to erotic literature.
121836338
Wave front evolution and equivariant Morse lemma
122633217
Poisson structures on the plane and other powers of volume forms
The hierarchy of formsf(dx1∧...∧dxn)α (α fixed) starts with the series A, D, and E. Their singular hypersurfaces admit quasihomogéneous polynomials g as representatives. The dimension of the space of moduli of forms with fixed g is calculated; it is equal to the number of monomials h, for which g(hx)α has weight zero. For Poisson structures on the plane (α=−1, n=2) this dimension is one less than the number of irreducible components of the curve g=0, i.e., is equal to the number h1,0 of mixed Hodge structures.
122136489
Spaces of functions with moderate singularities
117386543
Topologically Necessary Singularities on Moving Wavefronts and Caustics
In his posthumous Vorlesungen Uber Dynamik Jacobi claimed that the caustic (formed by the conjugate points of a given initial point along all the geodesics) on the surface of an ellipsoid has four cusps.
118067094
Singularities of smooth mappings with additional structures : collected papers