The Resource Singularities of Differentiable Maps, Volume 2 : Monodromy and Asymptotics of Integrals, by Elionora Arnold, S.M. Gusein-Zade, Alexander N. Varchenko, (electronic resource)

Singularities of Differentiable Maps, Volume 2 : Monodromy and Asymptotics of Integrals, by Elionora Arnold, S.M. Gusein-Zade, Alexander N. Varchenko, (electronic resource)

Label
Singularities of Differentiable Maps, Volume 2 : Monodromy and Asymptotics of Integrals
Title
Singularities of Differentiable Maps, Volume 2
Title remainder
Monodromy and Asymptotics of Integrals
Statement of responsibility
by Elionora Arnold, S.M. Gusein-Zade, Alexander N. Varchenko
Creator
Contributor
Author
Author
Subject
Language
  • eng
  • 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 still-relevant 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
Member of
http://library.link/vocab/creatorName
Arnold, Elionora
Dewey number
515
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
  • czQg3ehb_Pc
  • VU_Hnmw4xO0
  • rA_rbn76xgs
Language note
English
LC call number
QA299.6-433
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
  • Gusein-Zade, S.M.
  • Varchenko, Alexander N.
Series statement
Modern Birkhäuser Classics,
http://library.link/vocab/subjectName
  • Global analysis (Mathematics)
  • Geometry, algebraic
  • Global differential geometry
  • Topological Groups
  • Cell aggregation
  • Mathematics
  • Analysis
  • Algebraic Geometry
  • Differential Geometry
  • Topological Groups, Lie Groups
  • Manifolds and Cell Complexes (incl. Diff.Topology)
  • Applications of Mathematics
Label
Singularities of Differentiable Maps, Volume 2 : Monodromy and Asymptotics of Integrals, by Elionora Arnold, S.M. Gusein-Zade, Alexander N. Varchenko, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
Part I. The topological structure of isolated critical points of functions -- Introduction -- 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 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
Edition
1st ed. 2012.
Extent
1 online resource (499 p.)
Form of item
online
Isbn
9781280802614
Media category
computer
Media type code
c
Other control number
10.1007/978-0-8176-8343-6
Specific material designation
remote
System control number
  • (CKB)2550000000100663
  • (EBL)973763
  • (OCoLC)801364329
  • (SSID)ssj0000682213
  • (PQKBManifestationID)11406186
  • (PQKBTitleCode)TC0000682213
  • (PQKBWorkID)10678289
  • (PQKB)11319022
  • (DE-He213)978-0-8176-8343-6
  • (MiAaPQ)EBC973763
  • (EXLCZ)992550000000100663
Label
Singularities of Differentiable Maps, Volume 2 : Monodromy and Asymptotics of Integrals, by Elionora Arnold, S.M. Gusein-Zade, Alexander N. Varchenko, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
Part I. The topological structure of isolated critical points of functions -- Introduction -- 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 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
Edition
1st ed. 2012.
Extent
1 online resource (499 p.)
Form of item
online
Isbn
9781280802614
Media category
computer
Media type code
c
Other control number
10.1007/978-0-8176-8343-6
Specific material designation
remote
System control number
  • (CKB)2550000000100663
  • (EBL)973763
  • (OCoLC)801364329
  • (SSID)ssj0000682213
  • (PQKBManifestationID)11406186
  • (PQKBTitleCode)TC0000682213
  • (PQKBWorkID)10678289
  • (PQKB)11319022
  • (DE-He213)978-0-8176-8343-6
  • (MiAaPQ)EBC973763
  • (EXLCZ)992550000000100663

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