Singularities of Differentiable Maps, Volume 1

Classification of Critical Points, Caustics and Wave Fronts

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

Part of the Modern Birkhäuser Classics book series (MBC)

Table of contents

  1. Front Matter
    Pages i-xii
  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

About this book

Introduction

Originally published in the 1980s, Singularities of Differentiable Maps: The Classification of Critical Points, Caustics and Wave Fronts was the first of two volumes that together formed a translation of the authors' influential Russian monograph on singularity theory.  This uncorrected softcover reprint of the work brings its still-relevant content back into the literature, making it available—and affordable—to a global audience of researchers and practitioners.

Singularity theory is a far-reaching extension of maxima and minima investigations of differentiable functions, with implications for many different areas of mathematics, engineering (catastrophe theory and the theory of bifurcations), and science.  The three parts of this first volume deal with the stability problem for smooth mappings, critical points of smooth functions, and caustics and wave front singularities.  Building on these concepts, the second volume (Monodromy and Asymptotics of Integrals) describes the topological and algebro-geometrical aspects of the theory, including monodromy, intersection forms, oscillatory integrals, asymptotics, and mixed Hodge structures of singularities.

Singularities of Differentiable Maps: The Classification of Critical Points, Caustics and Wave Fronts accommodates the needs of non-mathematicians, presupposing a limited mathematical background and beginning at an elementary level.  With this foundation, the book's sophisticated development permits readers to explore an unparalleled breadth of applications.

Keywords

caustic and wave front singularities critical points of smooth functions differentiable functions singularity theory stability problem for smooth mappings

Authors and affiliations

  • V.I. Arnold
    • 1
  • S.M. Gusein-Zade
    • 2
  • A.N. Varchenko
    • 3
  1. 1.Russian Academy of SciencesMoscowRussia
  2. 2.Moscow State UniversityMoscowRussia
  3. 3., Department MathematicsUniversity of North CarolinaChapel HillUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-8340-5
  • Copyright Information Springer Science+Business Media New York 2012
  • Publisher Name Birkhäuser, Boston
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-8339-9
  • Online ISBN 978-0-8176-8340-5
  • About this book
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