Symplectic invariants and Hamiltonian dynamics:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
1994
|
| Series: | Birkhäuser advanced texts
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 341 S. graph. Darst. |
| ISBN: | 3764350660 9783764350666 0817650660 |
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MARC
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| 100 | 1 | |a Hofer, Helmut |d 1956- |e Verfasser |0 (DE-588)141380551 |4 aut | |
| 245 | 1 | 0 | |a Symplectic invariants and Hamiltonian dynamics |c Helmut Hofer ; Eduard Zehnder |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 1994 | |
| 300 | |a XIII, 341 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Birkhäuser advanced texts | |
| 650 | 4 | |a Hamiltonsches System - Symplektische Invariante | |
| 650 | 0 | 7 | |a Hamiltonsches System |0 (DE-588)4139943-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Symplektische Invariante |0 (DE-588)4350963-0 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Symplektische Invariante |0 (DE-588)4350963-0 |D s |
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Record in the Search Index
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| adam_text |
Contents
1 Introduction
1.1 Symplcctic vector spaces 1
1.2 Symplcctic diffeomorphisms and Hamiltonian vector fields G
1.3 Hamiltonian vector fields and symplcctic manifolds 9
1.4 Periodic orbits on energy surfaces 18
1.5 Existence of a periodic orbit on a convex energy surface 23
1.6 The problem of symplcctic embeddings 31
1.7 Syniplectic classification of positive definite quadratic forms . 35
1.8 The orbit structure near an equilibrium, Birkhoff normal form . 42
2 Symplectic capacities
2.1 Definition and application to embeddings 51
2.2 Rigidity of symplectic diffeomorphisms 58
3 Existence of a capacity
3.1 Definition of the capacity c0 69
3.2 The minimax idea 77
3.3 The analytical setting 82
3.4 The existence of a critical point 91
3.5 Examples and illustrations 98
4 Existence of closed characteristics
4.1 Periodic solutions on energy surfaces 105
4.2 The characteristic line bundle of a hypersurface 113
4.3 Hypersurfaces of contact type, the Wcinstein conjecture 119
4.4 "Classical" Hamiltonian systems 127
4.5 The torus and Herman's Non Closing Lemma 137
5 Compactly supported symplectic mappings in K2"
5.1 A special metric d for a group V of
Hamiltonian diffeomorphisms 143
5.2 The action spectrum of a Hamiltonian map 151
5.3 A "universal" variational principle 154
5.4 A continuous section of the action spectrum bundle Kil
5.5 An inequality between the displacement energy
and the capacity 165
5.6 Comparison of the metric d on V with the C() inotric 173
5.7 Fixed points and geodesies on V 182
v
vi Contents
6 The Arnold conjecture, Floer homology and symplectic homology
6.1 The Arnold conjecture on symplectic fixed points 194
6.2 The model case of the torus 202
6.3 Gradient like flows on compact spaces 217
6.4 Elliptic methods and symplectic fixed points 222
6.5 Floor's appraoch to Morse theory for the action functional 250
6.6 Symplectic homology 265
Appendix
A.I Generating functions of symplectic mappings in R2n 273
A.2 Action angle coordinates, the Theorem of Arnold and Jost 278
A.3 Embeddings of H1'2(S1) and smoothness of the action 286
A.4 The Cauchy Riemann operator on the sphere 291
A.5 Elliptic estimates near the boundary and an application 298
A.6 The generalized similarity principle 302
A.7 The Brouwer degree 305
A.8 Continuity property of the Alexander Spanier cohomology 314
Index 321
Bibliography 327 |
| any_adam_object | 1 |
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| ctrlnum | (OCoLC)246860610 (DE-599)BVBBV009686526 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV009686526 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:02:31Z |
| institution | BVB |
| isbn | 3764350660 9783764350666 0817650660 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006406024 |
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| physical | XIII, 341 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Birkhäuser |
| record_format | marc |
| series2 | Birkhäuser advanced texts |
| spelling | Hofer, Helmut 1956- Verfasser (DE-588)141380551 aut Symplectic invariants and Hamiltonian dynamics Helmut Hofer ; Eduard Zehnder Basel [u.a.] Birkhäuser 1994 XIII, 341 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Birkhäuser advanced texts Hamiltonsches System - Symplektische Invariante Hamiltonsches System (DE-588)4139943-2 gnd rswk-swf Symplektische Invariante (DE-588)4350963-0 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 s Symplektische Invariante (DE-588)4350963-0 s DE-604 Zehnder, Eduard 1940-2024 Verfasser (DE-588)141997346 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006406024&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hofer, Helmut 1956- Zehnder, Eduard 1940-2024 Symplectic invariants and Hamiltonian dynamics Hamiltonsches System - Symplektische Invariante Hamiltonsches System (DE-588)4139943-2 gnd Symplektische Invariante (DE-588)4350963-0 gnd |
| subject_GND | (DE-588)4139943-2 (DE-588)4350963-0 |
| title | Symplectic invariants and Hamiltonian dynamics |
| title_auth | Symplectic invariants and Hamiltonian dynamics |
| title_exact_search | Symplectic invariants and Hamiltonian dynamics |
| title_full | Symplectic invariants and Hamiltonian dynamics Helmut Hofer ; Eduard Zehnder |
| title_fullStr | Symplectic invariants and Hamiltonian dynamics Helmut Hofer ; Eduard Zehnder |
| title_full_unstemmed | Symplectic invariants and Hamiltonian dynamics Helmut Hofer ; Eduard Zehnder |
| title_short | Symplectic invariants and Hamiltonian dynamics |
| title_sort | symplectic invariants and hamiltonian dynamics |
| topic | Hamiltonsches System - Symplektische Invariante Hamiltonsches System (DE-588)4139943-2 gnd Symplektische Invariante (DE-588)4350963-0 gnd |
| topic_facet | Hamiltonsches System - Symplektische Invariante Hamiltonsches System Symplektische Invariante |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006406024&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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