| Description |
1 online resource |
| Series |
Modern Birkhäuser classics |
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Modern Birkhäuser classics.
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| Contents |
Part 1. The Topological Structure of Isolated Critical Points of Functions -- Elements of the theory of Picard-Lefschetz -- The topology of the non-singular level set and the variation operator of a singularity -- The bifurcation sets and the monodromy group of a singularity -- The intersection matrices of singularities of functions of two variables -- The intersection forms of boundary singularities and the topology of complete intersections -- Part 2. Oscillatory Integrals -- Discussion of results -- Elementary integrals and the resolution of singularities of the phase -- Asymptotics and Newton polyhedra -- The singular index, examples -- Part 3. Integrals of Holomorphic forms over Vanishing cycles -- The simplest properties of the integrals -- Complex oscillatory integrals -- Integrals and differential equations -- The coefficients of series expansions of integrals, the weight and Hodge filtrations and the spectrum of a critical point -- The mixed Hodge structure of an isolated critical point of a holomorphic function -- The period map and the intersection form |
| Summary |
Annotation The present volume is the second in a two-volume set entitled Singularities of Differentiable Maps. While the first volume, subtitled Classification of Critical Points and originallypublishedas Volume82 in the Monographs in Mathematics series, contained the zoology of differentiable maps, that is, it was devoted to a description of what, where, and how singularities could be encountered, this second volume concentrates on elements of theanatomy and physiology of singularities of differentiable functions. The questions considered are about the structure of singularities and how they function |
| Analysis |
Mathematics |
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Geometry, algebraic |
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Topological Groups |
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Global analysis (Mathematics) |
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Global differential geometry |
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Algebraic Geometry |
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Differential Geometry |
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Topological Groups, Lie Groups |
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Manifolds and Cell Complexes (incl. Diff. Topology) |
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Applications of Mathematics |
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topologie |
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topology |
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wiskunde |
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toegepaste wiskunde |
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applied mathematics |
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analyse |
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analysis |
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differentiaalmeetkunde |
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Mathematics (General) |
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Wiskunde (algemeen) |
| Bibliography |
Includes bibliographical references and index |
| Subject |
Differentiable mappings.
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Singularities (Mathematics)
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Mathematics.
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Mathematical Concepts
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Mathematics
|
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mathematics.
|
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applied mathematics.
|
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Singularidades (Matemáticas)
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Matemáticas
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Mathematics
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Differentiable mappings
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Singularities (Mathematics)
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| Form |
Electronic book
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| Author |
Guseĭn-Zade, S. M. (Sabir Medzhidovich)
|
|
Varchenko, A. N. (Aleksandr Nikolaevich)
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| ISBN |
9780817683436 |
|
0817683437 |
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0817683429 |
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9780817683429 |
|
1280802618 |
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9781280802614 |
|
