Momentum maps and Hamiltonian reduction:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2004
|
| Series: | Progress in mathematics
222 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz.: S. [443] - 476 |
| Physical Description: | XXXIV, 497 S. Ill., graph. Darst. |
| ISBN: | 0817643079 3764343079 |
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| 100 | 1 | |a Ortega, Juan-Pablo |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Momentum maps and Hamiltonian reduction |c Juan-Pablo Ortega ; Tudor S. Ratiu |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2004 | |
| 300 | |a XXXIV, 497 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Progress in mathematics |v 222 | |
| 500 | |a Literaturverz.: S. [443] - 476 | ||
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| 650 | 4 | |a Systèmes hamiltoniens | |
| 650 | 4 | |a Global analysis (Mathematics) | |
| 650 | 4 | |a Global differential geometry | |
| 650 | 4 | |a Hamiltonian systems | |
| 650 | 4 | |a Lie groups | |
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Record in the Search Index
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| adam_text | Contents
Introduction xiii
1 Manifolds and Smooth Structures 1
1.1 Manifolds and smooth maps 1
1.2 Vector fields and Lie derivatives 17
1.3 Calculus on manifolds 20
1.4 Foliated spaces and distributions 27
1.5 Stratified spaces 30
1.6 Stratified spaces with smooth structure 32
1.7 Whitney stratifications 33
2 Lie Group Actions 37
2.1 Lie groups 37
2.2 Actions of Lie groups 51
2.3 Proper Lie group actions 59
2.4 The structure of proper G manifolds 75
2.5 The invariant functions of a proper G space 85
3 Pseudogroups and Groupoids 93
3.1 Pseudogroups of transformations 93
3.2 Pseudogroups generated by families of vector fields 95
3.3 Equivariant vector fields and invariant distributions 99
3.4 The saturated sets of an invariant distribution 105
3.5 Equivariant vector fields and isotropy type submanifolds 112
3.6 Groupoids 115
4 The Standard Momentum Map 121
4.1 Hamiltonian systems 121
4.2 Canonical Lie group and algebra actions 136
4.3 Momentum maps 140
4.4 The Chu momentum map 141
4.5 The standard momentum map 144
4.6 Momentum maps and isotropy type submanifolds 162
4.7 The convexity properties of momentum maps 168
x Contents
5 Generalizations of the Momentum Map 171
5.1 A short interlude on connections and holonomy 171
5.2 Cylinder valued momentum maps 174
5.3 Universal covering and covered spaces of a
symplectic Lie algebra action 181
5.4 Lie group valued momentum maps 188
5.5 The optimal momentum map 193
5.6 Momentum maps and groupoid moment maps 202
6 Regular Symplectic Reduction Theory 205
6.1 Point reduction 206
6.2 Coadjoint orbits as point reduced spaces 216
6.3 Orbit reduction 224
6.4 The regular reduction diagram 231
6.5 Reduction by shift 232
6.6 Cotangent bundle reduction 234
6.7 Reduction by stages 257
7 The Symplectic Slice Theorem 271
7.1 The Witt Artin decomposition 271
7.2 The symplectic tube 276
7.3 The G relative Darboux Theorem 279
7.4 The Symplectic Slice Theorem 281
7.5 The Symplectic Slice Theorem and standard momentum maps .... 282
7.6 A normal form for the cylinder valued momentum maps 287
7.7 The Reconstruction Equations 293
8 Singular Reduction and the Stratification Theorem 301
8.1 The symplectic strata 302
8.2 A structure theorem and Sjamaar s principle 309
8.3 The Symplectic Stratification Theorem 311
8.4 Singular orbit reduction 320
9 Optimal Reduction 331
9.1 Optimal point reduction 331
9.2 Optimal orbit reduction 337
9.3 Polar reduction 340
9.4 Optimal reduction by stages 349
9.5 Singular reduction by stages in the presence of a
standard momentum map 357
10 Poisson Reduction 363
10.1 Regular Poisson reduction 363
10.2 The reduction of a presheaf of Poisson algebras 366
10.3 Applications of the Poisson Reduction Theorem 10.2.5 373
10.4 Poisson reduction by distributions 380
10.5 Cosymplectic submanifolds and Dirac s formula 391
Contents xi
11 Dual Pairs 401
11.1 Regular dual pairs 401
11.2 Bifoliations 414
11.3 Singular dual pairs 422
11.4 Dual pairs and symplectic leaf correspondence 426
11.5 Hamiltonian Poisson subgroups 432
11.6 Dual pairs induced by canonical Lie group actions 434
Bibliography 443
Index 476
|
| adam_txt |
Contents
Introduction xiii
1 Manifolds and Smooth Structures 1
1.1 Manifolds and smooth maps 1
1.2 Vector fields and Lie derivatives 17
1.3 Calculus on manifolds 20
1.4 Foliated spaces and distributions 27
1.5 Stratified spaces 30
1.6 Stratified spaces with smooth structure 32
1.7 Whitney stratifications 33
2 Lie Group Actions 37
2.1 Lie groups 37
2.2 Actions of Lie groups 51
2.3 Proper Lie group actions 59
2.4 The structure of proper G manifolds 75
2.5 The invariant functions of a proper G space 85
3 Pseudogroups and Groupoids 93
3.1 Pseudogroups of transformations 93
3.2 Pseudogroups generated by families of vector fields 95
3.3 Equivariant vector fields and invariant distributions 99
3.4 The saturated sets of an invariant distribution 105
3.5 Equivariant vector fields and isotropy type submanifolds 112
3.6 Groupoids 115
4 The Standard Momentum Map 121
4.1 Hamiltonian systems 121
4.2 Canonical Lie group and algebra actions 136
4.3 Momentum maps 140
4.4 The Chu momentum map 141
4.5 The standard momentum map 144
4.6 Momentum maps and isotropy type submanifolds 162
4.7 The convexity properties of momentum maps 168
x Contents
5 Generalizations of the Momentum Map 171
5.1 A short interlude on connections and holonomy 171
5.2 Cylinder valued momentum maps 174
5.3 Universal covering and covered spaces of a
symplectic Lie algebra action 181
5.4 Lie group valued momentum maps 188
5.5 The optimal momentum map 193
5.6 Momentum maps and groupoid moment maps 202
6 Regular Symplectic Reduction Theory 205
6.1 Point reduction 206
6.2 Coadjoint orbits as point reduced spaces 216
6.3 Orbit reduction 224
6.4 The regular reduction diagram 231
6.5 Reduction by shift 232
6.6 Cotangent bundle reduction 234
6.7 Reduction by stages 257
7 The Symplectic Slice Theorem 271
7.1 The Witt Artin decomposition 271
7.2 The symplectic tube 276
7.3 The G relative Darboux Theorem 279
7.4 The Symplectic Slice Theorem 281
7.5 The Symplectic Slice Theorem and standard momentum maps . 282
7.6 A normal form for the cylinder valued momentum maps 287
7.7 The Reconstruction Equations 293
8 Singular Reduction and the Stratification Theorem 301
8.1 The symplectic strata 302
8.2 A structure theorem and Sjamaar's principle 309
8.3 The Symplectic Stratification Theorem 311
8.4 Singular orbit reduction 320
9 Optimal Reduction 331
9.1 Optimal point reduction 331
9.2 Optimal orbit reduction 337
9.3 Polar reduction 340
9.4 Optimal reduction by stages 349
9.5 Singular reduction by stages in the presence of a
standard momentum map 357
10 Poisson Reduction 363
10.1 Regular Poisson reduction 363
10.2 The reduction of a presheaf of Poisson algebras 366
10.3 Applications of the Poisson Reduction Theorem 10.2.5 373
10.4 Poisson reduction by distributions 380
10.5 Cosymplectic submanifolds and Dirac's formula 391
Contents xi
11 Dual Pairs 401
11.1 Regular dual pairs 401
11.2 Bifoliations 414
11.3 Singular dual pairs 422
11.4 Dual pairs and symplectic leaf correspondence 426
11.5 Hamiltonian Poisson subgroups 432
11.6 Dual pairs induced by canonical Lie group actions 434
Bibliography 443
Index 476 |
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| language | English |
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| spelling | Ortega, Juan-Pablo Verfasser aut Momentum maps and Hamiltonian reduction Juan-Pablo Ortega ; Tudor S. Ratiu Boston [u.a.] Birkhäuser 2004 XXXIV, 497 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 222 Literaturverz.: S. [443] - 476 Analyse globale (Mathématiques) Análise global larpcal Grupos de lie larpcal Géométrie différentielle globale Hamilton-vergelijkingen gtt Lie, Groupes de Sistemas hamiltonianos larpcal Systèmes hamiltoniens Global analysis (Mathematics) Global differential geometry Hamiltonian systems Lie groups Symplektische Geometrie (DE-588)4194232-2 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 gnd rswk-swf Symplektische Geometrie (DE-588)4194232-2 s Hamiltonsches System (DE-588)4139943-2 s DE-604 Ratiu, Tudor S. Verfasser aut Progress in mathematics 222 (DE-604)BV000004120 222 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014628952&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ortega, Juan-Pablo Ratiu, Tudor S. Momentum maps and Hamiltonian reduction Progress in mathematics Analyse globale (Mathématiques) Análise global larpcal Grupos de lie larpcal Géométrie différentielle globale Hamilton-vergelijkingen gtt Lie, Groupes de Sistemas hamiltonianos larpcal Systèmes hamiltoniens Global analysis (Mathematics) Global differential geometry Hamiltonian systems Lie groups Symplektische Geometrie (DE-588)4194232-2 gnd Hamiltonsches System (DE-588)4139943-2 gnd |
| subject_GND | (DE-588)4194232-2 (DE-588)4139943-2 |
| title | Momentum maps and Hamiltonian reduction |
| title_auth | Momentum maps and Hamiltonian reduction |
| title_exact_search | Momentum maps and Hamiltonian reduction |
| title_exact_search_txtP | Momentum maps and Hamiltonian reduction |
| title_full | Momentum maps and Hamiltonian reduction Juan-Pablo Ortega ; Tudor S. Ratiu |
| title_fullStr | Momentum maps and Hamiltonian reduction Juan-Pablo Ortega ; Tudor S. Ratiu |
| title_full_unstemmed | Momentum maps and Hamiltonian reduction Juan-Pablo Ortega ; Tudor S. Ratiu |
| title_short | Momentum maps and Hamiltonian reduction |
| title_sort | momentum maps and hamiltonian reduction |
| topic | Analyse globale (Mathématiques) Análise global larpcal Grupos de lie larpcal Géométrie différentielle globale Hamilton-vergelijkingen gtt Lie, Groupes de Sistemas hamiltonianos larpcal Systèmes hamiltoniens Global analysis (Mathematics) Global differential geometry Hamiltonian systems Lie groups Symplektische Geometrie (DE-588)4194232-2 gnd Hamiltonsches System (DE-588)4139943-2 gnd |
| topic_facet | Analyse globale (Mathématiques) Análise global Grupos de lie Géométrie différentielle globale Hamilton-vergelijkingen Lie, Groupes de Sistemas hamiltonianos Systèmes hamiltoniens Global analysis (Mathematics) Global differential geometry Hamiltonian systems Lie groups Symplektische Geometrie Hamiltonsches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014628952&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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