Encyclopaedia of Mathematical Sciences

Dynamical Systems VIII

Singularity Theory II. Applications

Editors: Arnol'd, V.I. (Ed.)

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About this book

In the first volume of this survey (Arnol'd et al. (1988), hereafter cited as "EMS 6") we acquainted the reader with the basic concepts and methods of the theory of singularities of smooth mappings and functions. This theory has numerous applications in mathematics and physics; here we begin describing these applica­ tions. Nevertheless the present volume is essentially independent of the first one: all of the concepts of singularity theory that we use are introduced in the course of the presentation, and references to EMS 6 are confined to the citation of technical results. Although our main goal is the presentation of analready formulated theory, the readerwill also come upon some comparatively recent results, apparently unknown even to specialists. We pointout some of these results. 2 3 In the consideration of mappings from C into C in§ 3. 6 of Chapter 1, we define the bifurcation diagram of such a mapping, formulate a K(n, 1)-theorem for the complements to the bifurcation diagrams of simple singularities, give the definition of the Mond invariant N in the spirit of "hunting for invariants", and we draw the reader's attention to a method of constructing the image of a mapping from the corresponding function on a manifold with boundary. In§ 4. 6 of the same chapter we introduce the concept of a versal deformation of a function with a nonisolated singularity in the dass of functions whose critical sets are arbitrary complete intersections of fixed dimension.

Reviews

V.I. Arnol’d, V.V. Goryunov, O.V. Lyashko, V.A. Vasil’ev, and V.I. Arnol’d (eds.)

Dynamical Systems VIII

"The book contains a huge amount of information from all the branches of Singularity Theory, presented in a very attractive way, with lots of inspiring pictures."

ZENTRALBLATT MATH


Table of contents (1 chapters)

  • Singularity Theory II Classification and Applications

    Arnol’d, V. I. (et al.)

    Pages 1-235

Buy this book

eBook $119.00
price for USA (gross)
  • ISBN 978-3-662-06798-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.00
price for USA
  • ISBN 978-3-540-53376-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $159.00
price for USA
  • ISBN 978-3-642-08101-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Dynamical Systems VIII
Book Subtitle
Singularity Theory II. Applications
Editors
  • V.I. Arnol'd
Translated by
Joel, J.S.
Series Title
Encyclopaedia of Mathematical Sciences
Series Volume
39
Copyright
1993
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-06798-7
DOI
10.1007/978-3-662-06798-7
Hardcover ISBN
978-3-540-53376-4
Softcover ISBN
978-3-642-08101-9
Series ISSN
0938-0396
Edition Number
1
Number of Pages
VI, 238
Additional Information
Original Russian edition published by Publisher VINITI, Moscow, 1989
Topics