American Mathematical Society TranslationsSeries 2 1992; 199 pp; hardcover Volume: 153 ISBN10: 0821875027 ISBN13: 9780821875025 List Price: US$130 Member Price: US$104 Order Code: TRANS2/153
 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 development, 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 mathematiciansas well as physicists, engineers, and other consumers of singularity theoryto the world of ideas and methods in this burgeoning area. Readership Mathematicians as well as physicists, engineers, and other consumers of singularity theory. 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'dshteĭn and V. A. Sobolev  Qualitative analysis of singularly perturbed systems of chemical kinetics
 V. V. Goryunov  Bifurcations with symmetries
 S. M. GuseĭnZade  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. Khovanskiĭ  Newton polyhedra (algebra and geometry)
