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Titel:	Singularities of caustics and wave fronts
Von:	by V. I. Arnold
Person:	Arnolʹd, V. I. 1937-2010 Verfasser aut
Hauptverfasser:	Arnolʹd, V. I. 1937-2010 (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Dordrecht u.a. Kluwer Acad. Publ. 1990
Schriftenreihe:	Mathematics and its applications 62
Schlagworte:	Differentialgeometrie Kaustik Singularität > Mathematik
Online-Zugang:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002708916&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Beschreibung:	Aus d. Russ. übers.
Beschreibung:	XIII, 259 S. Ill., graph. Darst.
ISBN:	0792310381

Internformat

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Datensatz im Suchindex

DE-BY-UBR_call_number	00/SK 370 A759 80/SK 370 A759
DE-BY-UBR_katkey	835478
DE-BY-UBR_location	UB Magazin UB Lesesaal Mathematik
DE-BY-UBR_media_number	069018146092 069007948453
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adam_text	Contents Series Editor s Preface v Introduction ix 1 Symplectic geometry 1 1.1 Symplectic manifolds 1 1.2 Submanifolds of symplectic manifolds 7 1.3 Lagrangian manifolds, fibrations, mappings, and singularities 14 2 Applications of the theory of Lagrangian singularities 21 2.1 Oscillatory integrals 21 2.2 Lattice points 27 2.3 Perestroikas of caustics 31 2.4 Perestroikas of optical caustics 35 2.5 Shock wave singularities and perestroikas of Maxwell sets 38 3 Contact geometry 43 3.1 Wave fronts 43 3.2 Singularities of fronts 51 3.3 Perestroikas of fronts 56 4 Convolution of invariants, and period maps 61 4.1 Vector fields tangent to fronts 61 4.2 Linearised convolution of invariants 66 4.3 Period maps 73 4.4 Intersection forms of period maps 78 4.5 Poisson structures 81 4.6 Principal period maps 84 5 Lagrangian and Legendre topology 87 5.1 Lagrangian and Legendre cobordism 88 5.2 Lagrangian and Legendre characteristic classes 96 viii 5.3 Topology of complex discriminants 102 5.4 Functions with mild singularities 108 5.5 Global properties of singularities 113 5.6 Topology of Lagrangian inclusions 115 6 Projections of surfaces, and singularities of apparent contours 123 6.1 Singularities of projections from a surface to the plane 123 6.2 Singularities of projections of complete intersections 129 6.3 Geometry of bifurcation diagrams 139 7 Obstacle problem 155 7.1 Asymptotic rays in symplectic geometry 157 7.2 Contact geometry of pairs of hypersurfaces 166 7.3 Unfurled swallowtails 172 7.4 Symplectic triads 186 7.5 Contact triads 193 7.6 Hypericosahedral singularity 199 7.7 Normal forms of singularities in the obstacle problem 208 8 Transformation of waves defined by hyperbolic variational principles219 8.1 Hyperbolic systems and their light hypersurfaces 220 8.2 Singularities of light hypersurfaces of variational systems 224 8.3 Contact normal forms of singularities of quadratic cones 228 8.4 Singularities of ray systems and wave fronts at nonstrict hyperbolic points 231 Bibliography 241 Index 255
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isbn	0792310381
language	English
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physical	XIII, 259 S. Ill., graph. Darst.
publishDate	1990
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publisher	Kluwer Acad. Publ.
record_format	marc
series2	Mathematics and its applications / Soviet series
spellingShingle	Arnolʹd, V. I. 1937-2010 Singularities of caustics and wave fronts Differentialgeometrie (DE-588)4012248-7 gnd Kaustik (DE-588)4135840-5 gnd Singularität Mathematik (DE-588)4077459-4 gnd
subject_GND	(DE-588)4012248-7 (DE-588)4135840-5 (DE-588)4077459-4
title	Singularities of caustics and wave fronts
title_auth	Singularities of caustics and wave fronts
title_exact_search	Singularities of caustics and wave fronts
title_full	Singularities of caustics and wave fronts by V. I. Arnold
title_fullStr	Singularities of caustics and wave fronts by V. I. Arnold
title_full_unstemmed	Singularities of caustics and wave fronts by V. I. Arnold
title_short	Singularities of caustics and wave fronts
title_sort	singularities of caustics and wave fronts
topic	Differentialgeometrie (DE-588)4012248-7 gnd Kaustik (DE-588)4135840-5 gnd Singularität Mathematik (DE-588)4077459-4 gnd
topic_facet	Differentialgeometrie Kaustik Singularität Mathematik
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002708916&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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work_keys_str_mv	AT arnolʹdvi singularitiesofcausticsandwavefronts

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