Dynamical Systems VIII: Singularity Theory II. Applications
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| Weitere Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1993
|
| Schriftenreihe: | Encyclopaedia of Mathematical Sciences
39 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 applications. 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 an already formulated theory, the reader will also come upon some comparatively recent results, apparently unknown even to specialists. We point out 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 |
| Beschreibung: | 1 Online-Ressource (VI, 238 p) |
| ISBN: | 9783662067987 9783642081019 |
| ISSN: | 0938-0396 |
| DOI: | 10.1007/978-3-662-06798-7 |
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| 245 | 1 | 0 | |a Dynamical Systems VIII |b Singularity Theory II. Applications |c edited by V. I. Arnol'd |
| 264 | 1 | |a Berlin, Heidelberg |b Springer Berlin Heidelberg |c 1993 | |
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| 500 | |a 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 applications. 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 an already formulated theory, the reader will also come upon some comparatively recent results, apparently unknown even to specialists. We point out 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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Datensatz im Suchindex
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| dewey-full | 514.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.2 |
| dewey-search | 514.2 |
| dewey-sort | 3514.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-06798-7 |
| format | Electronic eBook |
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| id | DE-604.BV042423386 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662067987 9783642081019 |
| issn | 0938-0396 |
| language | English |
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| spelling | Arnol'd, V. I. edt Dynamical Systems VIII Singularity Theory II. Applications edited by V. I. Arnol'd Berlin, Heidelberg Springer Berlin Heidelberg 1993 1 Online-Ressource (VI, 238 p) txt rdacontent c rdamedia cr rdacarrier Encyclopaedia of Mathematical Sciences 39 0938-0396 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 applications. 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 an already formulated theory, the reader will also come upon some comparatively recent results, apparently unknown even to specialists. We point out 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 Mathematics Geometry, algebraic Global analysis (Mathematics) Algebraic topology Cell aggregation / Mathematics Algebraic Topology Manifolds and Cell Complexes (incl. Diff.Topology) Analysis Theoretical, Mathematical and Computational Physics Algebraic Geometry Mathematik Encyclopaedia of Mathematical Sciences 39 (DE-604)BV024126459 39 https://doi.org/10.1007/978-3-662-06798-7 Verlag Volltext |
| spellingShingle | Dynamical Systems VIII Singularity Theory II. Applications Encyclopaedia of Mathematical Sciences Mathematics Geometry, algebraic Global analysis (Mathematics) Algebraic topology Cell aggregation / Mathematics Algebraic Topology Manifolds and Cell Complexes (incl. Diff.Topology) Analysis Theoretical, Mathematical and Computational Physics Algebraic Geometry Mathematik |
| title | Dynamical Systems VIII Singularity Theory II. Applications |
| title_auth | Dynamical Systems VIII Singularity Theory II. Applications |
| title_exact_search | Dynamical Systems VIII Singularity Theory II. Applications |
| title_full | Dynamical Systems VIII Singularity Theory II. Applications edited by V. I. Arnol'd |
| title_fullStr | Dynamical Systems VIII Singularity Theory II. Applications edited by V. I. Arnol'd |
| title_full_unstemmed | Dynamical Systems VIII Singularity Theory II. Applications edited by V. I. Arnol'd |
| title_short | Dynamical Systems VIII |
| title_sort | dynamical systems viii singularity theory ii applications |
| title_sub | Singularity Theory II. Applications |
| topic | Mathematics Geometry, algebraic Global analysis (Mathematics) Algebraic topology Cell aggregation / Mathematics Algebraic Topology Manifolds and Cell Complexes (incl. Diff.Topology) Analysis Theoretical, Mathematical and Computational Physics Algebraic Geometry Mathematik |
| topic_facet | Mathematics Geometry, algebraic Global analysis (Mathematics) Algebraic topology Cell aggregation / Mathematics Algebraic Topology Manifolds and Cell Complexes (incl. Diff.Topology) Analysis Theoretical, Mathematical and Computational Physics Algebraic Geometry Mathematik |
| url | https://doi.org/10.1007/978-3-662-06798-7 |
| volume_link | (DE-604)BV024126459 |
| work_keys_str_mv | AT arnoldvi dynamicalsystemsviiisingularitytheoryiiapplications |