Topological invariants of plane curves and caustics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[1994]
|
| Schriftenreihe: | University lecture series
Volume 5 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Auf dem Cover: "Dean Jacqueline B. Lewis memorial lectures, Rutgers University" |
| Beschreibung: | vii, 60 Seiten Diagramme |
| ISBN: | 0821803085 9780821803080 |
Internformat
MARC
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| 245 | 1 | 0 | |a Topological invariants of plane curves and caustics |c V. I. Arnold |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [1994] | |
| 264 | 4 | |c © 1994 | |
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| 650 | 0 | 7 | |a Topologische Invariante |0 (DE-588)4310559-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Glatte Kurve |0 (DE-588)4157470-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Ebene Kurve |0 (DE-588)4150970-5 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Lecture 1. Invariants and Discriminants of Plane Curves 1
Preface to Lecture 1 3
Chapter 1. Plane Curves 5
§1. The three basic invariants 5
§2. Properties of the basic invariants 8
§3. Computation of basic invariants 10
§4. Extremal curves and tree like curves 12
§5. The numerology 16
§6. Cobordisms 20
§7. Long curves 22
Chapter 2. Legendrian Knots 25
§8. From plane curves to Legendrian knots 25
§9. The space of Legendrian curves 27
§10. The basic invariant J+ 29
§11. The Legendrian linking numbers 31
§12. Calculation of linking numbers 32
Lecture 2. Symplectic and Contact Topology of Caustics and Wave
Fronts, and Sturm Theory 37
Chapter 3. Singularities of Caustics and Sturm Theory 39
§13. The Lagrangian collapse and the last geometrical theorem of
Jacobi 39
§14. The four cusp theorem 41
§15. Sturm theory and Morse theory 43
§16. Proof of the four cusps theorem 44
ChAPTER 4. Singularities of Wave Fronts and the Tennis Ball Theorem 47
§17. The wave fronts reversal 47
§18. The front reversal four cusps theorem 50
§19. The proof of the existence of four cusps on a front 52
§20. The tennis ball theorem 53
References
|
| 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 | BV010272143 |
| classification_rvk | SI 165 SK 260 SK 350 |
| ctrlnum | (OCoLC)260220324 (DE-599)BVBBV010272143 |
| discipline | Mathematik |
| format | Book |
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| genre_facet | Konferenzschrift |
| id | DE-604.BV010272143 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:49:37Z |
| institution | BVB |
| isbn | 0821803085 9780821803080 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006833520 |
| oclc_num | 260220324 |
| open_access_boolean | |
| owner | DE-12 DE-824 DE-355 DE-BY-UBR DE-739 DE-19 DE-BY-UBM DE-11 DE-91G DE-BY-TUM DE-384 DE-83 |
| owner_facet | DE-12 DE-824 DE-355 DE-BY-UBR DE-739 DE-19 DE-BY-UBM DE-11 DE-91G DE-BY-TUM DE-384 DE-83 |
| physical | vii, 60 Seiten Diagramme |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | University lecture series |
| series2 | University lecture series |
| spelling | Arnolʹd, V. I. 1937-2010 Verfasser (DE-588)119540878 aut Topological invariants of plane curves and caustics V. I. Arnold Providence, Rhode Island American Mathematical Society [1994] © 1994 vii, 60 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier University lecture series Volume 5 Auf dem Cover: "Dean Jacqueline B. Lewis memorial lectures, Rutgers University" Hamiltonsches System (DE-588)4139943-2 gnd rswk-swf Knotentheorie (DE-588)4164318-5 gnd rswk-swf Topologische Invariante (DE-588)4310559-2 gnd rswk-swf Glatte Kurve (DE-588)4157470-9 gnd rswk-swf Ebene Kurve (DE-588)4150970-5 gnd rswk-swf (DE-588)1071861417 Konferenzschrift gnd-content Hamiltonsches System (DE-588)4139943-2 s Ebene Kurve (DE-588)4150970-5 s Knotentheorie (DE-588)4164318-5 s DE-604 Glatte Kurve (DE-588)4157470-9 s Topologische Invariante (DE-588)4310559-2 s Erscheint auch als Online-Ausgabe 978-1-4704-2189-2 University lecture series Volume 5 (DE-604)BV004153846 5 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006833520&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Arnolʹd, V. I. 1937-2010 Topological invariants of plane curves and caustics University lecture series Hamiltonsches System (DE-588)4139943-2 gnd Knotentheorie (DE-588)4164318-5 gnd Topologische Invariante (DE-588)4310559-2 gnd Glatte Kurve (DE-588)4157470-9 gnd Ebene Kurve (DE-588)4150970-5 gnd |
| subject_GND | (DE-588)4139943-2 (DE-588)4164318-5 (DE-588)4310559-2 (DE-588)4157470-9 (DE-588)4150970-5 (DE-588)1071861417 |
| title | Topological invariants of plane curves and caustics |
| title_auth | Topological invariants of plane curves and caustics |
| title_exact_search | Topological invariants of plane curves and caustics |
| title_full | Topological invariants of plane curves and caustics V. I. Arnold |
| title_fullStr | Topological invariants of plane curves and caustics V. I. Arnold |
| title_full_unstemmed | Topological invariants of plane curves and caustics V. I. Arnold |
| title_short | Topological invariants of plane curves and caustics |
| title_sort | topological invariants of plane curves and caustics |
| topic | Hamiltonsches System (DE-588)4139943-2 gnd Knotentheorie (DE-588)4164318-5 gnd Topologische Invariante (DE-588)4310559-2 gnd Glatte Kurve (DE-588)4157470-9 gnd Ebene Kurve (DE-588)4150970-5 gnd |
| topic_facet | Hamiltonsches System Knotentheorie Topologische Invariante Glatte Kurve Ebene Kurve Konferenzschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006833520&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004153846 |
| work_keys_str_mv | AT arnolʹdvi topologicalinvariantsofplanecurvesandcaustics |