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Singularities of differentiable maps. Volume 1, Classification of critical points, caustics and wave fronts

Author: V I Arnolʹd; S M Guseĭn-Zade; A N Varchenko
Publisher: [New York] : Birkhäuser, ©2012.
Series: Modern Birkhäuser classics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:

This first of two volumes deals with the stability problem for smooth mappings, critical points of smooth functions, and caustics and wave front singularities, beginning at a basic level that  Read more...

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Genre/Form: Electronic books
Additional Physical Format: Printed edition:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: V I Arnolʹd; S M Guseĭn-Zade; A N Varchenko
ISBN: 9780817683405 0817683402
OCLC Number: 794672449
Notes: "Reprint of the 1985 edition."
Description: 1 online resource.
Contents: Part 1. Basic Concepts --
The simplest examples --
The classes åII --
The quadratic differential of a map --
The local algebra of a map and the Weierstrass preparation theorem --
The local multiplicity of a holomorphic map --
Stability and infinitesimal stability --
The proof of the stability theorem --
Versal deformations --
The classification of stable germs by genotype --
Review of further results --
Part 2. Critical Points of Smooth Functions --
A start to the classification of critical points --
Quasihomogeneous and semiquasihomogeneous singularities --
The classification of quasihomogeneous functions --
Spectral sequences for the reduction to normal forms --
Lists of singularities --
The determinator of singularities --
Real, symmetric and boundary singularities --
Part 3. The Singularities of Caustics and Wave Fronts --
Lagrangian singularities --
Generating families --
Legendrian singularities --
The classification of Lagrangian and Legendrian singularities --
Bifurcations of caustics and wave fronts.
Series Title: Modern Birkhäuser classics.
Other Titles: Osobennosty differentsüruemykh otobrazhenii.
Classification of critical points, caustics and wave fronts
Responsibility: V.I. Arnold, S.M. Gusein-Zade, A.N. Varchenko.

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