Singularities of differentiable maps, Volume 1 classification of critical points, caustics and wave fronts /
<p>Originally published in the 1980s, <i>Singularities of Differentiable Maps: The Classification of Critical Points, Caustics and Wave Fronts </i>was the first of two<i> </i>volumes that together formed a translation of the authors' influential Russian monograph o...
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| Format: | eBook |
| Language: | English |
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Boston
Springer
2012.
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| Series: | Modern Birkhäuser Classics
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| Online Access: | Click here to view the full text content |
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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.