**American Mathematical Society Translations - Series 2**

1992;
199 pp;
Hardcover

MSC: Primary 40; 51; 57; 58; 92;
Secondary 12; 19; 28; 32; 35; 49; 60

**Print ISBN: 978-0-8218-7502-5
Product Code: TRANS2/153**

List Price: $138.00

AMS Member Price: $110.40

MAA Member Price: $124.20

**Electronic ISBN: 978-1-4704-3364-2
Product Code: TRANS2/153.E**

List Price: $130.00

AMS Member Price: $104.00

MAA Member Price: $117.00

# Singularity Theory and Some Problems of Functional Analysis

Share this page *Edited by *
*S. G. Gindikin*

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 mathematicians—as well as physicists, engineers, and other consumers of singularity theory—to 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

## Singularity Theory and Some Problems of Functional Analysis

- Cover Cover11
- Title page iii4
- Copyright page iv5
- Contents v6
- Foreward vii8
- Period maps connected with a versal deformation of a critical point of a function, and the discriminant 110
- Characteristic classes of singularities 1120
- Lacunas of hyperbolic partial differential operators and singularity theory 2534
- Reflection groups in singularity theory 3948
- Qualitative analysis of singularly perturbed systems of chemical kinetics 7382
- Bifurcations with symmetries 93102
- Stratifications of function space and algebraic ๐พ-theory 109118
- Singularities in optimization problems 125134
- Nice dimensions and their generalizations in singularity theory 137146
- On an inverse problem of measure theory 149158
- Classes of coefficients of convergent random series in spaces ๐ฟ_{๐,๐} 159168
- Corner singularities and multidimensional folds in nonlinear analysis 173182
- Newton polyhedra (algebra and geometry) 183192
- Back Cover Back Cover1210