Singularity Theory I [Paperback]

This is a compact guide to the principles and main applications of Singularity Theory by one of the worlds top research groups. It includes a number of new results as well as a carefully prepared and extensive bibliography that makes it easy to find the necessary details. Its ideal for any mathematician or physicist interested in modern mathematical analysis.

From the reviews: ... My general impression is of a particularly nice book, with a well-balanced bibliography, recommended!
Mededelingen van Het Wiskundig Genootschap, 1995
... The authors offer here an up to date guide to the topic and its main applications, including a number of new results. It is very convenient for the reader, a carefully prepared and extensive bibliography ... makes it easy to find the necessary details when needed. The books (EMS 6 and EMS 39) describe a lot of interesting topics. ... Both volumes are a very valuable addition to the library of any mathematician or physicist interested in modern mathematical analysis.
European Mathematical Society Newsletter, 19941. Critical Points of Functions.- 1. Invariants of Critical Points.- 1.1. Degenerate and Nondegenerate Critical Points.- 1.2. Equivalence of Critical Points.- 1.3. Stable Equivalence.- 1.4. The Local Algebra and the Multiplicity of a Singularity.- 1.5. Finite Determinacy of an Isolated Singularity.- 1.6. Lie Group Actions on Manifolds.- 1.7. Versal Deformations of a Critical Point.- 1.8. Infinitesimal Versality.- 1.9. The Modality of a Critical Point.- 1.10. The Level Bifurcation Set.- 1.11. Truncated Versal Deformations and the Function Bifurcation Set.- 2. The Classification of Critical Points.- 2.1. Normal Forms.- 2.2. Classes of Low Modality.- 2.3. Singularities of Modality ? 2.- 2.4. Simple Singularities and Klein Singularities.- 2.5. Resolution of Simple Singularities.- 2.6. Unimodal and Bimodal Singularities.- 2.7. Adjacency of SingularlĐ