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Monographs in Mathematics

Singularities of Differentiable Maps

Volume I: The Classification of Critical Points Caustics and Wave Fronts

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

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  • ISBN 978-1-4612-5154-5
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Softcover $99.99
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  • ISBN 978-1-4612-9589-1
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About this book

... there is nothing so enthralling, so grandiose, nothing that stuns or captivates the human soul quite so much as a first course in a science. After the first five or six lectures one already holds the brightest hopes, already sees oneself as a seeker after truth. I too have wholeheartedly pursued science passionately, as one would a beloved woman. I was a slave, and sought no other sun in my life. Day and night I crammed myself, bending my back, ruining myself over my books; I wept when I beheld others exploiting science fot personal gain. But I was not long enthralled. The truth is every science has a beginning, but never an end - they go on for ever like periodic fractions. Zoology, for example, has discovered thirty-five thousand forms of life ... A. P. Chekhov. "On the road" In this book a start is made to the "zoology" of the singularities of differentiable maps. This theory is a young branch of analysis which currently occupies a central place in mathematics; it is the crossroads of paths leading from very abstract corners of mathematics (such as algebraic and differential geometry and topology, Lie groups and algebras, complex manifolds, commutative algebra and the like) to the most applied areas (such as differential equations and dynamical systems, optimal control, the theory of bifurcations and catastrophes, short-wave and saddle-point asymptotics and geometrical and wave optics).

Table of contents (22 chapters)

  • The simplest examples

    Arnold, V. I. (et al.)

    Pages 3-26

  • The classes Σ 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 $79.99
price for USA in USD (gross)
  • ISBN 978-1-4612-5154-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.99
price for USA in USD
  • ISBN 978-1-4612-9589-1
  • Free shipping for individuals worldwide
  • 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 I: The Classification of Critical Points Caustics and Wave Fronts
Authors
Series Title
Monographs in Mathematics
Series Volume
82
Copyright
1985
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston, Inc.
eBook ISBN
978-1-4612-5154-5
DOI
10.1007/978-1-4612-5154-5
Softcover ISBN
978-1-4612-9589-1
Series ISSN
1017-0480
Edition Number
1
Number of Pages
396
Topics