Index theory for symplectic paths with applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
2002
|
| Schriftenreihe: | Progress in mathematics
207 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 361 - 373 |
| Beschreibung: | XXIV, 380 S. graph. Darst. |
| ISBN: | 3764366478 |
Internformat
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| 245 | 1 | 0 | |a Index theory for symplectic paths with applications |c Yiming Long |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2002 | |
| 300 | |a XXIV, 380 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in mathematics |v 207 | |
| 500 | |a Literaturverz. S. 361 - 373 | ||
| 650 | 4 | |a Index, Théorie de l' (Mathématiques) | |
| 650 | 4 | |a Itération (Mathématiques) | |
| 650 | 4 | |a Systèmes hamiltoniens | |
| 650 | 4 | |a Variétés symplectiques | |
| 650 | 4 | |a Hamiltonian systems | |
| 650 | 4 | |a Index theory (Mathematics) | |
| 650 | 4 | |a Iterative methods (Mathematics) | |
| 650 | 4 | |a Symplectic manifolds | |
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Datensatz im Suchindex
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| adam_text | Contents
Preface ix
Introduction . xi
I The Symplectic Group Sp(2n) 1
1 Algebraic Aspects 3
1.1 Symplectic matrices 3
1.2 Symplectic spaces 7
1.3 Eigenvalues of symplectic matrices 9
1.4 Normal forms for the eigenvalue 1 16
1.5 Normal forms for the eigenvalue 1 24
1.6 Normal forms for eigenvalues in U R 25
1.7 Normal forms for eigenvalues outside U 34
1.8 Basic normal forms 36
1.9 Perturbations basic normal forms 42
2 Topological Aspects 48
2.1 Structures of Sp(2) and its subsets 48
2.2 The global structure of Sp(2n,R) 51
2.3 Hyperbolic symplectic matrix set 54
2.4 Structure of regular sets 58
2.5 Structures of singular sets 67
2.6 Transversality of rotation paths 69
2.7 Orientability of MM(2n) in Sp(2n) 73
II The Variational Method 79
3 Hamiltonian Systems and Canonical Transformations 81
3.1 Canonical transformations 81
3.2 Generating functions 85
4 The Variational Functional 91
4.1 The Galerkin approximation 91
4.2 The L2 Variational Structure 95
4.3 The saddle point reduction 97
4.4 The dimension theorem on kernels 102
4.5 Certain estimates 104
III Index Theory 109
5 Index Functions for Symplectic Paths 111
5.1 Paths in Sp(2) 112
5.2 Non degenerate paths in Sp(2n) 116
5.3 Index properties of non degenerate paths 120
5.4 Perturbations of degenerate paths 123
vi Contents
6 Properties of Index Functions 132
6.1 Index functions and Morse indices 132
6.2 An axiom approach and further properties 145
7 Relations with other Morse Indices 152
7.1 The Galerkin approximation 152
7.2 Second order Hamiltonian systems 162
7.3 Lagrangian systems 167
IV Iteration Theory 175
8 Precise Iteration Formulae 177
8.1 Paths in Sp(2) 178
8.2 Hyperbolic and elliptic paths 184
8.3 General symplectic paths 188
9 Bott type Iteration Formulae 190
9.1 Splitting numbers 190
9.2 Bott type formulae 199
9.3 Abstract precise iteration formulae 204
10 Iteration Inequalities 209
10.1 Estimates via mean index and initial index 209
10.2 Successive estimates 215
10.3 Controlling iteration numbers via indices 223
11 The Common Index Jump Theorem 229
11.1 A common selection theorem 229
11.2 The common index jump theorem 235
12 Index Iteration Theory for Closed Geodesies 242
12.1 Morse index theory 243
12.2 Splitting numbers 247
V Applications 255
13 The Rabinowitz Conjecture 257
13.1 Minimax principle preparations 258
13.2 Controlling the minimal period via indices 262
13.3 Asymptotically linear Hamiltonian systems 264
13.4 Superquadratic Hamiltonian systems 271
13.5 Second order systems 280
13.6 Subharmonics 285
13.7 Notes and comments 288
14 Periodic Lagrangian Orbits on Tori 290
14.1 Critical module preparations 292
14.2 The finite energy homology theory 296
vii
14.3 Critical modules and isomorphisms 300
14.4 Global homological injectivity 305
14.5 Global homological vanishing 308
14.6 Notes and comments 313
15 Closed Characteristics on Convex Hypersurfaces 315
15.1 Index theorem for dual action principle 321
15.2 Variational properties 325
15.3 Critical orbits and index jumps 329
15.4 Existence and multiplicity 336
15.5 Stability results 341
15.6 Symmetric hypersurfaces 347
15.7 Notes and comments 354
Bibliography 361
Index 375
|
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| dewey-ones | 514 - Topology |
| dewey-raw | 514/.74 |
| dewey-search | 514/.74 |
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| id | DE-604.BV014160216 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:58:45Z |
| institution | BVB |
| isbn | 3764366478 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009705728 |
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| physical | XXIV, 380 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Long, Yiming Verfasser (DE-588)123540585 aut Index theory for symplectic paths with applications Yiming Long Basel [u.a.] Birkhäuser 2002 XXIV, 380 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 207 Literaturverz. S. 361 - 373 Index, Théorie de l' (Mathématiques) Itération (Mathématiques) Systèmes hamiltoniens Variétés symplectiques Hamiltonian systems Index theory (Mathematics) Iterative methods (Mathematics) Symplectic manifolds Hamiltonsches System (DE-588)4139943-2 gnd rswk-swf Indextheorie (DE-588)4161489-6 gnd rswk-swf Periodische Lösung (DE-588)4199269-6 gnd rswk-swf Symplektische Gruppe (DE-588)4276585-7 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 s Periodische Lösung (DE-588)4199269-6 s Symplektische Gruppe (DE-588)4276585-7 s Indextheorie (DE-588)4161489-6 s DE-604 Progress in mathematics 207 (DE-604)BV000004120 207 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009705728&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Long, Yiming Index theory for symplectic paths with applications Progress in mathematics Index, Théorie de l' (Mathématiques) Itération (Mathématiques) Systèmes hamiltoniens Variétés symplectiques Hamiltonian systems Index theory (Mathematics) Iterative methods (Mathematics) Symplectic manifolds Hamiltonsches System (DE-588)4139943-2 gnd Indextheorie (DE-588)4161489-6 gnd Periodische Lösung (DE-588)4199269-6 gnd Symplektische Gruppe (DE-588)4276585-7 gnd |
| subject_GND | (DE-588)4139943-2 (DE-588)4161489-6 (DE-588)4199269-6 (DE-588)4276585-7 |
| title | Index theory for symplectic paths with applications |
| title_auth | Index theory for symplectic paths with applications |
| title_exact_search | Index theory for symplectic paths with applications |
| title_full | Index theory for symplectic paths with applications Yiming Long |
| title_fullStr | Index theory for symplectic paths with applications Yiming Long |
| title_full_unstemmed | Index theory for symplectic paths with applications Yiming Long |
| title_short | Index theory for symplectic paths with applications |
| title_sort | index theory for symplectic paths with applications |
| topic | Index, Théorie de l' (Mathématiques) Itération (Mathématiques) Systèmes hamiltoniens Variétés symplectiques Hamiltonian systems Index theory (Mathematics) Iterative methods (Mathematics) Symplectic manifolds Hamiltonsches System (DE-588)4139943-2 gnd Indextheorie (DE-588)4161489-6 gnd Periodische Lösung (DE-588)4199269-6 gnd Symplektische Gruppe (DE-588)4276585-7 gnd |
| topic_facet | Index, Théorie de l' (Mathématiques) Itération (Mathématiques) Systèmes hamiltoniens Variétés symplectiques Hamiltonian systems Index theory (Mathematics) Iterative methods (Mathematics) Symplectic manifolds Hamiltonsches System Indextheorie Periodische Lösung Symplektische Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009705728&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
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