Dynamical Systems VIII
Singularity Theory II. Applications
Seiten
2010
|
1. Softcover reprint of hardcover 1st ed. 1993
Springer Berlin (Verlag)
978-3-642-08101-9 (ISBN)
Springer Berlin (Verlag)
978-3-642-08101-9 (ISBN)
In the first volume of this survey (Arnol'd et al. (1988), hereafter cited as "EMS 6") we acquainted the reader with the basic concepts and methods of the theory of singularities of smooth mappings and functions. This theory has numerous applications in mathematics and physics; here we begin describing these applica tions. Nevertheless the present volume is essentially independent of the first one: all of the concepts of singularity theory that we use are introduced in the course of the presentation, and references to EMS 6 are confined to the citation of technical results. Although our main goal is the presentation of analready formulated theory, the readerwill also come upon some comparatively recent results, apparently unknown even to specialists. We pointout some of these results. 2 3 In the consideration of mappings from C into C in
3. 6 of Chapter 1, we define the bifurcation diagram of such a mapping, formulate a K(n, 1)-theorem for the complements to the bifurcation diagrams of simple singularities, give the definition of the Mond invariant N in the spirit of "hunting for invariants", and we draw the reader's attention to a method of constructing the image of a mapping from the corresponding function on a manifold with boundary. In
4. 6 of the same chapter we introduce the concept of a versal deformation of a function with a nonisolated singularity in the dass of functions whose critical sets are arbitrary complete intersections of fixed dimension.
3. 6 of Chapter 1, we define the bifurcation diagram of such a mapping, formulate a K(n, 1)-theorem for the complements to the bifurcation diagrams of simple singularities, give the definition of the Mond invariant N in the spirit of "hunting for invariants", and we draw the reader's attention to a method of constructing the image of a mapping from the corresponding function on a manifold with boundary. In
4. 6 of the same chapter we introduce the concept of a versal deformation of a function with a nonisolated singularity in the dass of functions whose critical sets are arbitrary complete intersections of fixed dimension.
Singularity Theory II Classification and Applications.
V.I. Arnol'd, V.V. Goryunov, O.V. Lyashko, V.A. Vasil'ev, and V.I. Arnol'd (eds.)
Dynamical Systems VIII
"The book contains a huge amount of information from all the branches of Singularity Theory, presented in a very attractive way, with lots of inspiring pictures."
-ZENTRALBLATT MATH
| Erscheint lt. Verlag | 19.10.2010 |
|---|---|
| Reihe/Serie | Encyclopaedia of Mathematical Sciences |
| Co-Autor | V.I. Arnol'd, V.V. Goryunov, O.V. Lyashko, V.A. Vasil'ev |
| Übersetzer | J.S. Joel |
| Zusatzinfo | VI, 238 p. |
| Verlagsort | Berlin |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 366 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| Schlagworte | Analysis • bifurcation sets • Bifurkationsmengen • generalized Picard-Lefschetz theory • manifold • Maximum • maxwell manifolds • Maxwellmannigfaltigkeiten • Singularitäten von Funktionen und Abbildungen • Singularitäten von Rändern von Differentialgleichu • Singularitäten von Rändern von Differentialgleichungen • singularitie • singularities of boundaries of differential equations • Singularities of functions and mappings |
| ISBN-10 | 3-642-08101-0 / 3642081010 |
| ISBN-13 | 978-3-642-08101-9 / 9783642081019 |
| Zustand | Neuware |
| Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
Gekrümmte Kurven und Flächen
Buch | Softcover (2024)
De Gruyter (Verlag)
CHF 76,90
Nielsen Methods, Covering Spaces, and Hyperbolic Groups
Buch | Softcover (2024)
De Gruyter (Verlag)
CHF 153,90
