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The Resource Singularities of Differentiable Maps, Volume 1 : Classification of Critical Points, Caustics and Wave Fronts, by V.I. Arnold, S.M. Gusein-Zade, Alexander N. Varchenko, (electronic resource)

Singularities of Differentiable Maps, Volume 1 : Classification of Critical Points, Caustics and Wave Fronts, by V.I. Arnold, S.M. Gusein-Zade, Alexander N. Varchenko, (electronic resource)

Creator
Author
Contributor
Summary
Originally published in the 1980s, Singularities of Differentiable Maps: The Classification of Critical Points, Caustics and Wave Fronts was the first 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. Singularity theory is a far-reaching extension of maxima and minima investigations of differentiable functions, with implications for many different areas of mathematics, engineering (catastrophe theory and the theory of bifurcations), and science. The three parts of this first volume deal with the stability problem for smooth mappings, critical points of smooth functions, and caustics and wave front singularities. Building on these concepts, the second volume (Monodromy and Asymptotics of Integrals) describes the topological and algebro-geometrical aspects of the theory, including monodromy, intersection forms, oscillatory integrals, asymptotics, and mixed Hodge structures of singularities. Singularities of Differentiable Maps: The Classification of Critical Points, Caustics and Wave Fronts accommodates the needs of non-mathematicians, presupposing a limited mathematical background and beginning at an elementary level. With this foundation, the book's sophisticated development permits readers to explore an unparalleled breadth of applications
Language
  • eng
  • eng
Work
Publication
Edition
1st ed. 2012.
Extent
1 online resource (392 p.)
Note
  • "Reprint of the 1985 edition."
  • "Originally published as vol. 82 in the series Monographs in mathematics."
  • "Originally published as Osobennosty differentsiiruemyky otobrazhenii. Moscow : Science, 1982."
Contents
  • Part I. Basic concepts
  • The simplest examples
  • The classes Sigma^ I
  • The quadratic differential of a map
  • The local algebra of a map and the Weierstrass preparation theorem
  • The local multiplicity of a holomorphic map
  • Stability and infinitesimal stability
  • The proof of the stability theorem
  • Versal deformations
  • The classification of stable germs by genotype
  • Review of further results
  • Part II. Critical points of smooth functions
  • A start to the classification of critical points
  • Quasihomogeneous and semiquasihomogeneous singularities
  • The classification of quasihomogeneous functions
  • Spectral sequences for the reduction to normal forms
  • Lists of singularities
  • The determinator of singularities
  • Real, symmetric and boundary singularities
  • Part III. Singularities of caustics and wave fronts
  • Lagrangian singularities
  • Generating families
  • Legendrian singularities
  • The classification of Lagrangian and Legendrian singularities
  • The bifurcation of caustics and wave fronts
  • References
  • Further references
  • Subject Index
Isbn
9780817683405
Instance
Label
Singularities of Differentiable Maps, Volume 1 : Classification of Critical Points, Caustics and Wave Fronts
Title
Singularities of Differentiable Maps, Volume 1
Title remainder
Classification of Critical Points, Caustics and Wave Fronts
Statement of responsibility
by V.I. 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: The Classification of Critical Points, Caustics and Wave Fronts was the first 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. Singularity theory is a far-reaching extension of maxima and minima investigations of differentiable functions, with implications for many different areas of mathematics, engineering (catastrophe theory and the theory of bifurcations), and science. The three parts of this first volume deal with the stability problem for smooth mappings, critical points of smooth functions, and caustics and wave front singularities. Building on these concepts, the second volume (Monodromy and Asymptotics of Integrals) describes the topological and algebro-geometrical aspects of the theory, including monodromy, intersection forms, oscillatory integrals, asymptotics, and mixed Hodge structures of singularities. Singularities of Differentiable Maps: The Classification of Critical Points, Caustics and Wave Fronts accommodates the needs of non-mathematicians, presupposing a limited mathematical background and beginning at an elementary level. With this foundation, the book's sophisticated development permits readers to explore an unparalleled breadth of applications
Member of
http://library.link/vocab/creatorName
Arnold, V.I
Dewey number
515
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
  • cJCCHAenETw
  • 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 1 : Classification of Critical Points, Caustics and Wave Fronts, by V.I. Arnold, S.M. Gusein-Zade, Alexander N. Varchenko, (electronic resource)
Instantiates
Publication
Note
  • "Reprint of the 1985 edition."
  • "Originally published as vol. 82 in the series Monographs in mathematics."
  • "Originally published as Osobennosty differentsiiruemyky otobrazhenii. Moscow : Science, 1982."
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. Basic concepts -- The simplest examples -- The classes Sigma^ I -- The quadratic differential of a map -- The local algebra of a map and the Weierstrass preparation theorem -- The local multiplicity of a holomorphic map -- Stability and infinitesimal stability -- The proof of the stability theorem -- Versal deformations -- The classification of stable germs by genotype -- Review of further results -- Part II. Critical points of smooth functions -- A start to the classification of critical points -- Quasihomogeneous and semiquasihomogeneous singularities -- The classification of quasihomogeneous functions -- Spectral sequences for the reduction to normal forms -- Lists of singularities -- The determinator of singularities -- Real, symmetric and boundary singularities -- Part III. Singularities of caustics and wave fronts -- Lagrangian singularities -- Generating families -- Legendrian singularities -- The classification of Lagrangian and Legendrian singularities -- The bifurcation of caustics and wave fronts -- References -- Further references -- Subject Index
Dimensions
unknown
Edition
1st ed. 2012.
Extent
1 online resource (392 p.)
Form of item
online
Isbn
9780817683405
Media category
computer
Media type code
c
Other control number
10.1007/978-0-8176-8340-5
Specific material designation
remote
System control number
  • (CKB)2550000000103502
  • (EBL)973762
  • (OCoLC)801364323
  • (SSID)ssj0000682212
  • (PQKBManifestationID)11447402
  • (PQKBTitleCode)TC0000682212
  • (PQKBWorkID)10663752
  • (PQKB)10696116
  • (DE-He213)978-0-8176-8340-5
  • (MiAaPQ)EBC973762
  • (EXLCZ)992550000000103502
Label
Singularities of Differentiable Maps, Volume 1 : Classification of Critical Points, Caustics and Wave Fronts, by V.I. Arnold, S.M. Gusein-Zade, Alexander N. Varchenko, (electronic resource)
Publication
Note
  • "Reprint of the 1985 edition."
  • "Originally published as vol. 82 in the series Monographs in mathematics."
  • "Originally published as Osobennosty differentsiiruemyky otobrazhenii. Moscow : Science, 1982."
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. Basic concepts -- The simplest examples -- The classes Sigma^ I -- The quadratic differential of a map -- The local algebra of a map and the Weierstrass preparation theorem -- The local multiplicity of a holomorphic map -- Stability and infinitesimal stability -- The proof of the stability theorem -- Versal deformations -- The classification of stable germs by genotype -- Review of further results -- Part II. Critical points of smooth functions -- A start to the classification of critical points -- Quasihomogeneous and semiquasihomogeneous singularities -- The classification of quasihomogeneous functions -- Spectral sequences for the reduction to normal forms -- Lists of singularities -- The determinator of singularities -- Real, symmetric and boundary singularities -- Part III. Singularities of caustics and wave fronts -- Lagrangian singularities -- Generating families -- Legendrian singularities -- The classification of Lagrangian and Legendrian singularities -- The bifurcation of caustics and wave fronts -- References -- Further references -- Subject Index
Dimensions
unknown
Edition
1st ed. 2012.
Extent
1 online resource (392 p.)
Form of item
online
Isbn
9780817683405
Media category
computer
Media type code
c
Other control number
10.1007/978-0-8176-8340-5
Specific material designation
remote
System control number
  • (CKB)2550000000103502
  • (EBL)973762
  • (OCoLC)801364323
  • (SSID)ssj0000682212
  • (PQKBManifestationID)11447402
  • (PQKBTitleCode)TC0000682212
  • (PQKBWorkID)10663752
  • (PQKB)10696116
  • (DE-He213)978-0-8176-8340-5
  • (MiAaPQ)EBC973762
  • (EXLCZ)992550000000103502

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