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Singularities of Differentiable Maps

Volume I: The Classification of Critical Points Caustics and Wave Fronts

  • Authors
  • V. I. Arnold
  • S. M. Gusein-Zade
  • A. N. Varchenko

Part of the Monographs in Mathematics book series (MMA, volume 82)

Table of contents

  1. Front Matter
    Pages i-x
  2. Basic Concepts

    1. Front Matter
      Pages 1-1
    2. V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko
      Pages 3-26
    3. V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko
      Pages 27-59
    4. V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko
      Pages 60-71
    5. V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko
      Pages 72-83
    6. V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko
      Pages 84-114
    7. V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko
      Pages 115-132
    8. V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko
      Pages 133-144
    9. V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko
      Pages 145-156
    10. V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko
      Pages 157-172
    11. V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko
      Pages 173-182
  3. Critical Points of Smooth Functions

    1. Front Matter
      Pages 183-186
    2. V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko
      Pages 187-191
    3. V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko
      Pages 192-216
    4. V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko
      Pages 217-230
    5. V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko
      Pages 231-241
    6. V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko
      Pages 242-257
    7. V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko
      Pages 258-271
    8. V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko
      Pages 272-284
  4. The Singularities of Caustics and Wave Fronts

    1. Front Matter
      Pages 285-285
    2. V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko
      Pages 287-297
    3. V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko
      Pages 298-309
    4. V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko
      Pages 310-324
    5. V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko
      Pages 325-345
    6. V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko
      Pages 346-359
  5. Back Matter
    Pages 360-382

About this book

Introduction

... there is nothing so enthralling, so grandiose, nothing that stuns or captivates the human soul quite so much as a first course in a science. After the first five or six lectures one already holds the brightest hopes, already sees oneself as a seeker after truth. I too have wholeheartedly pursued science passionately, as one would a beloved woman. I was a slave, and sought no other sun in my life. Day and night I crammed myself, bending my back, ruining myself over my books; I wept when I beheld others exploiting science fot personal gain. But I was not long enthralled. The truth is every science has a beginning, but never an end - they go on for ever like periodic fractions. Zoology, for example, has discovered thirty-five thousand forms of life ... A. P. Chekhov. "On the road" In this book a start is made to the "zoology" of the singularities of differentiable maps. This theory is a young branch of analysis which currently occupies a central place in mathematics; it is the crossroads of paths leading from very abstract corners of mathematics (such as algebraic and differential geometry and topology, Lie groups and algebras, complex manifolds, commutative algebra and the like) to the most applied areas (such as differential equations and dynamical systems, optimal control, the theory of bifurcations and catastrophes, short-wave and saddle-point asymptotics and geometrical and wave optics).

Keywords

Lie Topology algebra differential geometry equation geometry manifold mathematics

Bibliographic information