April 18, 2002

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The European Singularities Network.

Arnold's Seminars in Paris , in Moscow.

Singularity Theory @ Isaac Newton Institute for Mathematical Sciences, July to December 2000 - Preprints.

Publications by V. I. Arnold on Singularity Theory:

• Theory of Singularities and its Applications, 1991.
• Singularities of Caustics and Wave Fronts, 1990.

BibTeX references.

In this book, which is based on lectures given in Pisa under the auspices of the Accademia Nazionale dei Lincei, the distinguished mathematician Vladimir Arnold describes those singularities encountered in different branches of mathematics. He avoids giving difficult proofs of all the results in order to provide the reader with a concise and accessible overview of the many guises and areas in which singularities appear, such as geometry and optics; optimal control theory and algebraic geometry; reflection groups and dynamical systems and many more. This will be an excellent companion for final year undergraduates and graduates whose area of study brings them into contact with singularities.

Part I. The Zoo of Singularities:

1. Morse theory of functions;
2. Whitney theory of mappings;
3. The Whitney-Cayley umbrella;
4. The swallowtail;
5. The discriminants of the reflection groups;
6. The icosahedron and the obstacle by-passing problem;
7. The unfurled swallowtail;
8. The folded and open umbrellas;
9. The singularities of projections and of the apparent contours;

Part II. Singularities of Bifurcation Diagrams:

10. Bifurcation diagrams of families of functions;
11. Stability boundary;
12. Ellipticity boundary and minima functions;
13. Hyperbolicity boundary;
14. Disconjugate equations, Tchebyshev system boundaries and Schubert singularities in flag manifolds;
15. Fundamental system boundaries, projective curve flattenings and Schubert singularities in Grassmann manifolds.

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