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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.Read more
- Arnold - world famous mathematician - has published lots of books - e.g. Springer, MIT
- First book in prestigious new series which covers ALL sciences. Books are based on lectures by top people
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- Date Published: June 1991
- format: Paperback
- isbn: 9780521422802
- length: 74 pages
- dimensions: 240 x 170 x 8 mm
- weight: 0.194kg
- availability: Unavailable - out of print
Table of Contents
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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