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Monographs in Mathematics

Singularities of Differentiable Maps

Volume II Monodromy and Asymptotic Integrals

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

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About this book

The present. volume is the second volume of the book "Singularities of Differentiable Maps" by V.1. Arnold, A. N. Varchenko and S. M. Gusein-Zade. The first volume, subtitled "Classification of critical points, caustics and wave fronts", was published by Moscow, "Nauka", in 1982. It will be referred to in this text simply as "Volume 1". Whilst the first volume contained the zoology of differentiable maps, that is it was devoted to a description of what, where and how singularities could be encountered, this volume contains the elements of the anatomy and physiology of singularities of differentiable functions. This means that the questions considered in it are about the structure of singularities and how they function. Another distinctive feature of the present volume is that we take a hard look at questions for which it is important to work in the complex domain, where the first volume was devoted to themes for which, on the whole, it was not important which field (real or complex) we were considering. Such topics as, for example, decomposition of singularities, the connection between singularities and Lie algebras and the asymptotic behaviour of different integrals depending on parameters become clearer in the complex domain. The book consists of three parts. In the first part we consider the topological structure of isolated critical points of holomorphic functions. We describe the fundamental topological characteristics of such critical points: vanishing cycles, distinguished bases, intersection matrices, monodromy groups, the variation operator and their interconnections and method of calculation.

Table of contents (16 chapters)

Table of contents (16 chapters)

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-1-4612-3940-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $109.99
price for USA in USD
  • ISBN 978-1-4612-8408-6
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Singularities of Differentiable Maps
Book Subtitle
Volume II Monodromy and Asymptotic Integrals
Authors
Series Title
Monographs in Mathematics
Series Volume
83
Copyright
1988
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-3940-6
DOI
10.1007/978-1-4612-3940-6
Softcover ISBN
978-1-4612-8408-6
Series ISSN
1017-0480
Edition Number
1
Number of Pages
VIII, 492
Number of Illustrations
5 b/w illustrations
Topics

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