Singularities of Differentiable Maps, Volume 1 Classification of Critical Points, Caustics and Wave Fronts
Originally published in the 1980s, Singularities of Differentiable Maps: The Classification of Critical Points, Caustics and Wave Fronts was the first of two volumes that together formed a translation of the authors' influential Russian monograph on singularity theory. This uncorrected softcov...
Main Authors: | , , |
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Format: | eBook |
Language: | English |
Published: |
Boston, MA
Birkhäuser
2012, 2012
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Edition: | 1st ed. 2012 |
Series: | Modern Birkhäuser Classics
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Subjects: | |
Online Access: | |
Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- Part I. Basic concepts
- The simplest examples
- The classes Sigma I
- 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 II. 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 III. Singularities of caustics and wave fronts
- Lagrangian singularities
- Generating families
- Legendrian singularities
- The classification of Lagrangian and Legendrian singularities
- The bifurcation of caustics and wave fronts
- References
- Further references
- Subject Index