Modern Birkhäuser Classics

Singularities of Differentiable Maps, Volume 1

Classification of Critical Points, Caustics and Wave Fronts

Authors: Arnold, V.I., Gusein-Zade, S.M., Varchenko, Alexander N.

  • Affordable reprint of a classic monograph written by experts in the field
  • Provides a uniquely sophisticated investigation of the topics discussed 
  • Useful for a wide range of applications across disciplines in fields such as differential equations, dynamical systems, optimal control, and optics
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  • ISBN 978-0-8176-8340-5
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About this book

​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 of a two-volume set deal with the stability problem for smooth mappings, critical points of smooth functions, and caustics and wave front singularities.  The second volume describes the topological and algebro-geometrical aspects of the theory: monodromy, intersection forms, oscillatory integrals, asymptotics, and mixed Hodge structures of singularities.

The first volume has been adapted for 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 more applications than previous books on singularities.

Table of contents (22 chapters)

  • The simplest examples

    Arnold, V. I. (et al.)

    Pages 3-26

  • The classes $$ \sum^{I} $$

    Arnold, V. I. (et al.)

    Pages 27-59

  • The quadratic differential of a map

    Arnold, V. I. (et al.)

    Pages 60-71

  • The local algebra of a map and the Weierstrass preparation theorem

    Arnold, V. I. (et al.)

    Pages 72-83

  • The local multiplicity of a holomorphic map

    Arnold, V. I. (et al.)

    Pages 84-114

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-0-8176-8340-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.00
price for USA
  • ISBN 978-0-8176-8339-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Singularities of Differentiable Maps, Volume 1
Book Subtitle
Classification of Critical Points, Caustics and Wave Fronts
Authors
Series Title
Modern Birkhäuser Classics
Copyright
2012
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-0-8176-8340-5
DOI
10.1007/978-0-8176-8340-5
Softcover ISBN
978-0-8176-8339-9
Series ISSN
2197-1803
Edition Number
1
Number of Pages
XII, 282
Number of Illustrations and Tables
67 b/w illustrations
Topics