The emergence of singularity theory marks the return of mathematics to the study of the simplest analytical objects: functions, graphs, curves, surfaces. The modern singularity theory for smooth mappings, which is currently undergoing intensive developments, can be thought of as a crossroad where the most abstract topics (such as algebraic and differential geometry and topology, complex analysis, invariant theory, and Lie group theory) meet the most applied topics (such as dynamical systems, mathematical physics, geometrical optics, mathematical economics, and control theory). The papers in this volume include reviews of established areas as well as presentations of recent results in singularity theory. The authors have paid special attention to examples and discussion of results rather than burying the ideas in formalism, notation, and technical details. The aim is to introduce all mathematicians - as well as physicists, engineers, and other consumers of singularity theory - to the world of ideas and methods in this burgeoning area.
Table of contents:
A. N. Varchenko: Period maps connected with a versal deformation of a critical point of a function, and the discriminant; V. A. Vassiliev: Characteristic classes of singularities; V. A. Vassiliev: Lacunas of hyperbolic partial differential operators and singularity theory; A. B. Givental: Reflection groups in singularity theory; V. M. Gol'dshtein and V. A. Sobolev: Qualitative analysis of singulary perturbed systems of chemical kinetics; V. V. Goryunov: Bifurcations with symmetries; S. M. Gusein-Zade: Stratifications of function space and algebraic K-theory; A. A. Davydov: Singularities in optimization problems; V. M. Zakalyukin: Nice dimensions and their generalizations in singularity theory; V. M. Klimkin: On an inverse problem of measure theory; S. Ya. Novikov: Classes of coefficients of convergent random series in spaces L[p[,[q; Yu. I. Sapronov: Corner singularities and multidimensional folds in nonlinear analysis; A. G. Khovanskii: Newton polyhedra (algebra and geometry).
Table of contents:
A. N. Varchenko: Period maps connected with a versal deformation of a critical point of a function, and the discriminant; V. A. Vassiliev: Characteristic classes of singularities; V. A. Vassiliev: Lacunas of hyperbolic partial differential operators and singularity theory; A. B. Givental: Reflection groups in singularity theory; V. M. Gol'dshtein and V. A. Sobolev: Qualitative analysis of singulary perturbed systems of chemical kinetics; V. V. Goryunov: Bifurcations with symmetries; S. M. Gusein-Zade: Stratifications of function space and algebraic K-theory; A. A. Davydov: Singularities in optimization problems; V. M. Zakalyukin: Nice dimensions and their generalizations in singularity theory; V. M. Klimkin: On an inverse problem of measure theory; S. Ya. Novikov: Classes of coefficients of convergent random series in spaces L[p[,[q; Yu. I. Sapronov: Corner singularities and multidimensional folds in nonlinear analysis; A. G. Khovanskii: Newton polyhedra (algebra and geometry).