Singularities of Differentiable Maps, Volume 1

Classification of Critical Points, Caustics and Wave Fronts

Authors:

ISBN: 978-0-8176-8339-9 (Print) 978-0-8176-8340-5 (Online)

Table of contents (22 chapters)

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  1. Front Matter

    Pages i-xii

  2. Basic Concepts

    1. Front Matter

      Pages 1-1

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      Pages 3-26

      The simplest examples

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      Pages 27-59

      The classes $ \sum^{I} $

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      Pages 60-71

      The quadratic differential of a map

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      Pages 72-83

      The local algebra of a map and the Weierstrass preparation theorem

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      Pages 84-114

      The local multiplicity of a holomorphic map

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      Pages 115-132

      Stability and infinitesimal stability

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      Pages 133-144

      The proof of the stability theorem

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      Pages 145-156

      Versal deformations

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      Pages 157-172

      The classification of stable germs by genotype

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      Pages 173-182

      Review of further results

  3. Critical points of smooth functions

    1. Front Matter

      Pages 183-186

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      Pages 187-191

      A start to the classification of critical points

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      Pages 192-216

      Quasihomogeneous and semiquasihomogeneous singularities

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      Pages 217-230

      The classification of quasihomogeneous functions

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      Pages 231-241

      Spectral sequences for the reduction to normal forms

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      Pages 242-257

      Lists of singularities

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      Pages 258-271

      The determinator of singularities

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      Pages 272-284

      Real, symmetric and boundary singularities

  4. Singularities of causties and wave fronts

    1. Front Matter

      Pages 285-285

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      Book Chapter

      Pages 287-297

      Lagrangian singularities

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      Pages 298-309

      Generating families

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      Pages 310-324

      Legendrian singularities

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