Singularities of Differentiable Maps: Volume II Monodromy and Asymptotic Integrals
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Boston, MA
Birkhäuser Boston
1988
|
| Series: | Monographs in Mathematics
83 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | The present. volume is the second volume of the book "Singularities of Differentiable Maps" by V.1. Arnold, A. N. Varchenko and S. M. Gusein-Zade. The first volume, subtitled "Classification of critical points, caustics and wave fronts", was published by Moscow, "Nauka", in 1982. It will be referred to in this text simply as "Volume 1". Whilst the first volume contained the zoology of differentiable maps, that is it was devoted to a description of what, where and how singularities could be encountered, this volume contains the elements of the anatomy and physiology of singularities of differentiable functions. This means that the questions considered in it are about the structure of singularities and how they function. Another distinctive feature of the present volume is that we take a hard look at questions for which it is important to work in the complex domain, where the first volume was devoted to themes for which, on the whole, it was not important which field (real or complex) we were considering. Such topics as, for example, decomposition of singularities, the connection between singularities and Lie algebras and the asymptotic behaviour of different integrals depending on parameters become clearer in the complex domain. The book consists of three parts. In the first part we consider the topological structure of isolated critical points of holomorphic functions. We describe the fundamental topological characteristics of such critical points: vanishing cycles, distinguished bases, intersection matrices, monodromy groups, the variation operator and their interconnections and method of calculation |
| Physical Description: | 1 Online-Ressource (VIII, 492 p.) 5 illus |
| ISBN: | 9781461239406 9781461284086 |
| DOI: | 10.1007/978-1-4612-3940-6 |
Staff View
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
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| dewey-sort | 3516.36 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-3940-6 |
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| id | DE-604.BV042420178 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:06Z |
| institution | BVB |
| isbn | 9781461239406 9781461284086 |
| language | English |
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| physical | 1 Online-Ressource (VIII, 492 p.) 5 illus |
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| publishDate | 1988 |
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| spelling | Arnolʹd, V. I. 1937-2010 Verfasser (DE-588)119540878 aut Singularities of Differentiable Maps Volume II Monodromy and Asymptotic Integrals edited by V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko Boston, MA Birkhäuser Boston 1988 1 Online-Ressource (VIII, 492 p.) 5 illus txt rdacontent c rdamedia cr rdacarrier Monographs in Mathematics 83 The present. volume is the second volume of the book "Singularities of Differentiable Maps" by V.1. Arnold, A. N. Varchenko and S. M. Gusein-Zade. The first volume, subtitled "Classification of critical points, caustics and wave fronts", was published by Moscow, "Nauka", in 1982. It will be referred to in this text simply as "Volume 1". Whilst the first volume contained the zoology of differentiable maps, that is it was devoted to a description of what, where and how singularities could be encountered, this volume contains the elements of the anatomy and physiology of singularities of differentiable functions. This means that the questions considered in it are about the structure of singularities and how they function. Another distinctive feature of the present volume is that we take a hard look at questions for which it is important to work in the complex domain, where the first volume was devoted to themes for which, on the whole, it was not important which field (real or complex) we were considering. Such topics as, for example, decomposition of singularities, the connection between singularities and Lie algebras and the asymptotic behaviour of different integrals depending on parameters become clearer in the complex domain. The book consists of three parts. In the first part we consider the topological structure of isolated critical points of holomorphic functions. We describe the fundamental topological characteristics of such critical points: vanishing cycles, distinguished bases, intersection matrices, monodromy groups, the variation operator and their interconnections and method of calculation Mathematics Global differential geometry Cell aggregation / Mathematics Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Gusejn-Zade, Sabir M. Sonstige (DE-588)170920453 oth Varčenko, Aleksandr N. 1949- Sonstige (DE-588)115203257 oth https://doi.org/10.1007/978-1-4612-3940-6 Verlag Volltext |
| spellingShingle | Arnolʹd, V. I. 1937-2010 Singularities of Differentiable Maps Volume II Monodromy and Asymptotic Integrals Mathematics Global differential geometry Cell aggregation / Mathematics Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik |
| title | Singularities of Differentiable Maps Volume II Monodromy and Asymptotic Integrals |
| title_auth | Singularities of Differentiable Maps Volume II Monodromy and Asymptotic Integrals |
| title_exact_search | Singularities of Differentiable Maps Volume II Monodromy and Asymptotic Integrals |
| title_full | Singularities of Differentiable Maps Volume II Monodromy and Asymptotic Integrals edited by V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko |
| title_fullStr | Singularities of Differentiable Maps Volume II Monodromy and Asymptotic Integrals edited by V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko |
| title_full_unstemmed | Singularities of Differentiable Maps Volume II Monodromy and Asymptotic Integrals edited by V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko |
| title_short | Singularities of Differentiable Maps |
| title_sort | singularities of differentiable maps volume ii monodromy and asymptotic integrals |
| title_sub | Volume II Monodromy and Asymptotic Integrals |
| topic | Mathematics Global differential geometry Cell aggregation / Mathematics Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik |
| topic_facet | Mathematics Global differential geometry Cell aggregation / Mathematics Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik |
| url | https://doi.org/10.1007/978-1-4612-3940-6 |
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