Dynamical Systems VIII : Singularity Theory II. Applications / edited by V. I. Arnol’d
(Encyclopaedia of Mathematical Sciences ; 39)
| データ種別 | 電子ブック |
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| 出版情報 | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer , 1993 |
| 本文言語 | 英語 |
| 大きさ | VI, 238 p : online resource |
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| 一般注記 | 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 |
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| 著者標目 | Arnol’d, V. I. editor SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Algebraic geometry LCSH:Mathematical analysis LCSH:Analysis (Mathematics) LCSH:Algebraic topology LCSH:Manifolds (Mathematics) LCSH:Complex manifolds LCSH:Physics FREE:Mathematics FREE:Algebraic Topology FREE:Manifolds and Cell Complexes (incl. Diff.Topology) FREE:Analysis FREE:Theoretical, Mathematical and Computational Physics FREE:Algebraic Geometry |
| 分 類 | DC23:514.2 |
| 巻冊次 | ISBN:9783662067987 
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| ISBN | 9783662067987 |
| URL | http://dx.doi.org/10.1007/978-3-662-06798-7 |
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