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Catastrophe Theory

  • Vladimir Igorevich Arnold

Table of contents

  1. Front Matter
    Pages i-xii
  2. Vladimir Igorevich Arnold
    Pages 1-2
  3. Vladimir Igorevich Arnold
    Pages 3-6
  4. Vladimir Igorevich Arnold
    Pages 7-9
  5. Vladimir Igorevich Arnold
    Pages 10-13
  6. Vladimir Igorevich Arnold
    Pages 14-19
  7. Vladimir Igorevich Arnold
    Pages 29-38
  8. Vladimir Igorevich Arnold
    Pages 39-42
  9. Vladimir Igorevich Arnold
    Pages 43-46
  10. Vladimir Igorevich Arnold
    Pages 47-56
  11. Vladimir Igorevich Arnold
    Pages 57-62
  12. Vladimir Igorevich Arnold
    Pages 63-65
  13. Vladimir Igorevich Arnold
    Pages 66-74
  14. Vladimir Igorevich Arnold
    Pages 75-78
  15. Back Matter
    Pages 79-79

About this book

Introduction

Singularity theory is growing very fast and many new results have been discovered since the Russian edition appeared: for instance the relation of the icosahedron to the problem of by­ passing a generic obstacle. The reader can find more details about this in the articles "Singularities of ray systems" and "Singularities in the calculus of variations" listed in the bi­ bliography of the present edition. Moscow, September 1983 v. I. Arnold Preface to the Russian Edition "Experts discuss forecasting disasters" said a New York Times report on catastrophe theory in November 1977. The London Times declared Catastrophe Theory to be the "main intellectual movement of the century" while an article on catastrophe theory in Science was headed "The emperor has no clothes". This booklet explains what catastrophe theory is about and why it arouses such controversy. It also contains non-con­ troversial results from the mathematical theories of singulari­ ties and bifurcation. The author has tried to explain the essence of the fundamen­ tal results and applications to readers having minimal mathe­ matical background but the reader is assumed to have an in­ quiring mind. Moscow 1981 v. I. Arnold Contents Chapter 1. Singularities, Bifurcations, and Catastrophe Theories ............... 1 Chapter 2. Whitney's Singularity Theory ... 3 Chapter 3. Applications of Whitney's Theory 7 Chapter 4. A Catastrophe Machine ...... 10 Chapter 5. Bifurcations of Equilibrium States 14 Chapter 6. Loss of Stability of Equilibrium and the Generation of Auto-Oscillations . . . . . . 20 .

Keywords

Bifurcations Calc Catastrophe Theory Katastrophe Katastrophentheorie Mathematica Microsoft Access Optimierungsprobleme Optimization Problems Singularities Singularitäten Verzweigung calculus function singularity theory

Authors and affiliations

  • Vladimir Igorevich Arnold
    • 1
  1. 1.Department of MathematicsUniversity of MoscowMoscowUSSR

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-96799-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 1984
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-12859-5
  • Online ISBN 978-3-642-96799-3
  • Buy this book on publisher's site