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The Resource Singularities of differentiable maps, Volume 2, Monodromy and asymptotics of integrals, V. I. Arnold, S.M. GuseinZade, A.N. Varchenko, (electronic resource)
Singularities of differentiable maps, Volume 2, Monodromy and asymptotics of integrals, V. I. Arnold, S.M. GuseinZade, A.N. Varchenko, (electronic resource)
Resource Information
The item Singularities of differentiable maps, Volume 2, Monodromy and asymptotics of integrals, V. I. Arnold, S.M. GuseinZade, A.N. Varchenko, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item Singularities of differentiable maps, Volume 2, Monodromy and asymptotics of integrals, V. I. Arnold, S.M. GuseinZade, A.N. Varchenko, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Summary
 Originally published in the 1980s, Singularities of Differentiable Maps: Monodromy and Asymptotics of Integrals was the second of two volumes that together formed a translation of the authors' influential Russian monograph on singularity theory. This uncorrected softcover reprint of the work brings its stillrelevant content back into the literature, making it available—and affordable—to a global audience of researchers and practitioners. While the first volume of this title, subtitled Classification of Critical Points, Caustics and Wave Fronts, contained the zoology of differentiable maps—that is, was devoted to a description of what, where, and how singularities could be encountered—this second volume concentrates on elements of the anatomy and physiology of singularities of differentiable functions. The questions considered here are about the structure of singularities and how they function. In the first part the authors consider the topological structure of isolated critical points of holomorphic functions: vanishing cycles; distinguished bases; intersection matrices; monodromy groups; the variation operator; and their interconnections and method of calculation. The second part is devoted to the study of the asymptotic behavior of integrals of the method of stationary phase, which is widely met within applications. The third and last part deals with integrals evaluated over level manifolds in a neighborhood of the critical point of a holomorphic function. This monograph is suitable for mathematicians, researchers, postgraduates, and specialists in the areas of mechanics, physics, technology, and other sciences dealing with the theory of singularities of differentiable maps
 Language

 eng
 rus
 eng
 Extent
 1 online resource.
 Note
 "Reprint of the 1988 edition." Cover
 Contents

 Part I. The topological structure of isolated critical points of functions
 Introduction
 Elements of the theory of PicardLefschetz
 The topology of the nonsingular 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 II. Oscillatory integrals
 Discussion of results
 Elementary integrals and the resolution of singularities of the phase
 Asymptotics and Newton polyhedra
 The singular index, examples
 Part III. 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 weighted 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
 References
 Subject Index
 Isbn
 9780817683436
 Label
 Singularities of differentiable maps, Volume 2, Monodromy and asymptotics of integrals
 Title
 Singularities of differentiable maps
 Title number
 Volume 2
 Title part
 Monodromy and asymptotics of integrals
 Statement of responsibility
 V. I. Arnold, S.M. GuseinZade, A.N. Varchenko
 Title variation
 Monodromy and asymptotics of integrals
 Subject

 Global differential geometry.
 Mathematical Concepts
 Singularities (Mathematics)
 Mathematics
 Mathematics
 Topological Groups.
 Differentiable mappings
 Singularities (Mathematics)
 Singularities (Mathematics)
 Electronic resources
 Differentiable mappings
 Topological Groups, Lie Groups.
 Differentiable mappings
 Geometry, algebraic.
 Differential Geometry.
 Singularities (Mathematics)
 Mathematical Concepts
 Singularities (Mathematics)
 Mathematics.
 Manifolds and Cell Complexes (incl. Diff.Topology).
 Singularities (Mathematics)
 Global analysis (Mathematics).
 Differentiable mappings
 Applications of Mathematics.
 Differentiable mappings
 Differentiable mappings
 Algebraic Geometry.
 Language

 eng
 rus
 eng
 Summary
 Originally published in the 1980s, Singularities of Differentiable Maps: Monodromy and Asymptotics of Integrals was the second of two volumes that together formed a translation of the authors' influential Russian monograph on singularity theory. This uncorrected softcover reprint of the work brings its stillrelevant content back into the literature, making it available—and affordable—to a global audience of researchers and practitioners. While the first volume of this title, subtitled Classification of Critical Points, Caustics and Wave Fronts, contained the zoology of differentiable maps—that is, was devoted to a description of what, where, and how singularities could be encountered—this second volume concentrates on elements of the anatomy and physiology of singularities of differentiable functions. The questions considered here are about the structure of singularities and how they function. In the first part the authors consider the topological structure of isolated critical points of holomorphic functions: vanishing cycles; distinguished bases; intersection matrices; monodromy groups; the variation operator; and their interconnections and method of calculation. The second part is devoted to the study of the asymptotic behavior of integrals of the method of stationary phase, which is widely met within applications. The third and last part deals with integrals evaluated over level manifolds in a neighborhood of the critical point of a holomorphic function. This monograph is suitable for mathematicians, researchers, postgraduates, and specialists in the areas of mechanics, physics, technology, and other sciences dealing with the theory of singularities of differentiable maps
 Cataloging source
 GW5XE
 http://library.link/vocab/creatorDate
 19372010
 http://library.link/vocab/creatorName
 Arnolʹd, V. I.
 Image bit depth
 0
 LC call number
 QA613.64
 LC item number
 .A76 2012
 Literary form
 non fiction
 Nature of contents
 dictionaries
 http://library.link/vocab/relatedWorkOrContributorName

 SpringerLink
 GuseĭnZade, S. M.
 Varchenko, A. N.
 Series statement
 Modern Birkhäuser Classics
 http://library.link/vocab/subjectName

 Mathematical Concepts
 Mathematics
 Differentiable mappings
 Singularities (Mathematics)
 Differentiable mappings
 Singularities (Mathematics)
 Label
 Singularities of differentiable maps, Volume 2, Monodromy and asymptotics of integrals, V. I. Arnold, S.M. GuseinZade, A.N. Varchenko, (electronic resource)
 Note
 "Reprint of the 1988 edition." Cover
 Antecedent source
 mixed
 Bibliography note
 Includes bibliographical references and index
 Color
 not applicable
 Contents
 Part I. The topological structure of isolated critical points of functions  Introduction  Elements of the theory of PicardLefschetz  The topology of the nonsingular 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 II. Oscillatory integrals  Discussion of results  Elementary integrals and the resolution of singularities of the phase  Asymptotics and Newton polyhedra  The singular index, examples  Part III. 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 weighted 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  References  Subject Index
 Dimensions
 unknown
 Extent
 1 online resource.
 File format
 multiple file formats
 Form of item

 online
 electronic
 Isbn
 9780817683436
 Level of compression
 uncompressed
 Other control number
 10.1007/9780817683436
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number

 (OCoLC)794177587
 (OCoLC)ocn794177587
 Label
 Singularities of differentiable maps, Volume 2, Monodromy and asymptotics of integrals, V. I. Arnold, S.M. GuseinZade, A.N. Varchenko, (electronic resource)
 Note
 "Reprint of the 1988 edition." Cover
 Antecedent source
 mixed
 Bibliography note
 Includes bibliographical references and index
 Color
 not applicable
 Contents
 Part I. The topological structure of isolated critical points of functions  Introduction  Elements of the theory of PicardLefschetz  The topology of the nonsingular 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 II. Oscillatory integrals  Discussion of results  Elementary integrals and the resolution of singularities of the phase  Asymptotics and Newton polyhedra  The singular index, examples  Part III. 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 weighted 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  References  Subject Index
 Dimensions
 unknown
 Extent
 1 online resource.
 File format
 multiple file formats
 Form of item

 online
 electronic
 Isbn
 9780817683436
 Level of compression
 uncompressed
 Other control number
 10.1007/9780817683436
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number

 (OCoLC)794177587
 (OCoLC)ocn794177587
Subject
 Algebraic Geometry.
 Applications of Mathematics.
 Differentiable mappings
 Differentiable mappings
 Differentiable mappings
 Differentiable mappings
 Differentiable mappings
 Differentiable mappings
 Differential Geometry.
 Electronic resources
 Geometry, algebraic.
 Global analysis (Mathematics).
 Global differential geometry.
 Manifolds and Cell Complexes (incl. Diff.Topology).
 Mathematical Concepts
 Mathematical Concepts
 Mathematics
 Mathematics
 Mathematics.
 Singularities (Mathematics)
 Singularities (Mathematics)
 Singularities (Mathematics)
 Singularities (Mathematics)
 Singularities (Mathematics)
 Singularities (Mathematics)
 Topological Groups, Lie Groups.
 Topological Groups.
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