Singularities of caustics and wave fronts:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht u.a.
Kluwer Acad. Publ.
1990
|
| Series: | Mathematics and its applications / Soviet series
62 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus d. Russ. übers. |
| Physical Description: | XIII, 259 S. Ill., graph. Darst. |
| ISBN: | 0792310381 |
Staff View
MARC
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| 264 | 1 | |a Dordrecht u.a. |b Kluwer Acad. Publ. |c 1990 | |
| 300 | |a XIII, 259 S. |b Ill., graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804118543617228800 |
|---|---|
| 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
|
| any_adam_object | 1 |
| author | Arnolʹd, V. I. 1937-2010 |
| author_GND | (DE-588)119540878 |
| author_facet | Arnolʹd, V. I. 1937-2010 |
| author_role | aut |
| author_sort | Arnolʹd, V. I. 1937-2010 |
| author_variant | v i a vi via |
| building | Verbundindex |
| bvnumber | BV004362761 |
| classification_rvk | SK 370 |
| ctrlnum | (OCoLC)246570414 (DE-599)BVBBV004362761 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV004362761 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:11:58Z |
| institution | BVB |
| isbn | 0792310381 |
| language | English |
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| physical | XIII, 259 S. Ill., graph. Darst. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series2 | Mathematics and its applications / Soviet series |
| spelling | Arnolʹd, V. I. 1937-2010 Verfasser (DE-588)119540878 aut Singularities of caustics and wave fronts by V. I. Arnold Dordrecht u.a. Kluwer Acad. Publ. 1990 XIII, 259 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications / Soviet series 62 Aus d. Russ. übers. Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Kaustik (DE-588)4135840-5 gnd rswk-swf Singularität Mathematik (DE-588)4077459-4 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 s Singularität Mathematik (DE-588)4077459-4 s DE-604 Kaustik (DE-588)4135840-5 s Soviet series Mathematics and its applications 62 (DE-604)BV004708148 62 HBZ Datenaustausch application/pdf 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 Inhaltsverzeichnis |
| 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 |