Nearly integrable infinite dimensional Hamiltonian systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1993
|
| Schriftenreihe: | Lecture notes in mathematics
1556 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXVII, 101 S. |
| ISBN: | 3540571612 0387571612 |
Internformat
MARC
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| 100 | 1 | |a Kuksin, Sergej B. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Nearly integrable infinite dimensional Hamiltonian systems |c Sergej B. Kuksin |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1993 | |
| 300 | |a XXVII, 101 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1556 | |
| 650 | 0 | 7 | |a Hamiltonsches System |0 (DE-588)4139943-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Integrables System |0 (DE-588)4114032-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Unendlichdimensionales System |0 (DE-588)4207956-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Hamilton-Gleichungen |0 (DE-588)4289066-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Hamilton-Gleichungen |0 (DE-588)4289066-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Hamiltonsches System |0 (DE-588)4139943-2 |D s |
| 689 | 1 | 1 | |a Unendlichdimensionales System |0 (DE-588)4207956-1 |D s |
| 689 | 1 | 2 | |a Integrables System |0 (DE-588)4114032-1 |D s |
| 689 | 1 | |5 DE-604 | |
| 830 | 0 | |a Lecture notes in mathematics |v 1556 |w (DE-604)BV000676446 |9 1556 | |
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| 940 | 1 | |n oe | |
Datensatz im Suchindex
| _version_ | 1805082758285885440 |
|---|---|
| adam_text |
Contents
Introduction vii
1. Finite dimensional situation viii
2. Infinite dimensional systems (the problem and the result) xi
3. Applications xvi
4. Remarks on averaging theorems xxv
5. Remarks on nearly integrable symplectomorphisms xxv
6. Notations xxvii
Part 1. Symplectic structures and Hamiltonian
systems in scales of Hilbert spaces 1
1.1. Symplectic Hilbert scales and Hamiltonian equations 1
1.2. Canonical transformations 6
1.3. Local solvability of Hamiltonian equations 9
1.4. Toroidal phase space 11
1.5. A version of the former constructions 12
Part 2. Statement of the main theorem and its consequences 13
2.1. Statement of the main theorem 14
2.2. Reformulation of Theorem 1.1 18
2.3. Nonlinear Schrodinger equation 22
2.4. Schrodinger equation with random potential 28
2.5. Nonlinear Schrodinger equation on the real line 33
2.6. Nonlinear string equation 35
2.7. On non commuting operators J, A and partially hyperbolic invariant tori 39
Appendix. On superposition operator in Sobolev spaces 44
Part 3. Proof of the main theorem 45
3.1. Preliminary transformations 45
3.2. Proof of Theorem 1.1 53
3.3. Proof of Lemma 2.2 (solving the homological equations) 67
3.4. Proof of Lemma 3.1 (estimation of the small divisors) 73
3.5. Proof of Lemma 2.3 (estimation of the change of variables) 78
3.6. Proof of Refinement 2 82
3.7. On reducibility of variational equations 84
3.8. Proof of Theorem 1.2 85
Appendix A. Interpolation theorem 91
Appendix B. Some estimates for Fourier series 92
Appendix C. Lipschitz homeomorphisms of Borel sets 92
Appendix D. Cauchy estimate 93
List of notations 94
Bibliography 96
Index 101 |
| any_adam_object | 1 |
| author | Kuksin, Sergej B. |
| author_facet | Kuksin, Sergej B. |
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| author_sort | Kuksin, Sergej B. |
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| classification_rvk | SI 850 |
| classification_tum | PHY 011f MAT 354f |
| ctrlnum | (OCoLC)246275715 (DE-599)BVBBV008220268 |
| discipline | Physik Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-20T07:37:45Z |
| institution | BVB |
| isbn | 3540571612 0387571612 |
| language | English |
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| physical | XXVII, 101 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Kuksin, Sergej B. Verfasser aut Nearly integrable infinite dimensional Hamiltonian systems Sergej B. Kuksin Berlin [u.a.] Springer 1993 XXVII, 101 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1556 Hamiltonsches System (DE-588)4139943-2 gnd rswk-swf Integrables System (DE-588)4114032-1 gnd rswk-swf Unendlichdimensionales System (DE-588)4207956-1 gnd rswk-swf Hamilton-Gleichungen (DE-588)4289066-4 gnd rswk-swf Hamilton-Gleichungen (DE-588)4289066-4 s DE-604 Hamiltonsches System (DE-588)4139943-2 s Unendlichdimensionales System (DE-588)4207956-1 s Integrables System (DE-588)4114032-1 s Lecture notes in mathematics 1556 (DE-604)BV000676446 1556 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005426803&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kuksin, Sergej B. Nearly integrable infinite dimensional Hamiltonian systems Lecture notes in mathematics Hamiltonsches System (DE-588)4139943-2 gnd Integrables System (DE-588)4114032-1 gnd Unendlichdimensionales System (DE-588)4207956-1 gnd Hamilton-Gleichungen (DE-588)4289066-4 gnd |
| subject_GND | (DE-588)4139943-2 (DE-588)4114032-1 (DE-588)4207956-1 (DE-588)4289066-4 |
| title | Nearly integrable infinite dimensional Hamiltonian systems |
| title_auth | Nearly integrable infinite dimensional Hamiltonian systems |
| title_exact_search | Nearly integrable infinite dimensional Hamiltonian systems |
| title_full | Nearly integrable infinite dimensional Hamiltonian systems Sergej B. Kuksin |
| title_fullStr | Nearly integrable infinite dimensional Hamiltonian systems Sergej B. Kuksin |
| title_full_unstemmed | Nearly integrable infinite dimensional Hamiltonian systems Sergej B. Kuksin |
| title_short | Nearly integrable infinite dimensional Hamiltonian systems |
| title_sort | nearly integrable infinite dimensional hamiltonian systems |
| topic | Hamiltonsches System (DE-588)4139943-2 gnd Integrables System (DE-588)4114032-1 gnd Unendlichdimensionales System (DE-588)4207956-1 gnd Hamilton-Gleichungen (DE-588)4289066-4 gnd |
| topic_facet | Hamiltonsches System Integrables System Unendlichdimensionales System Hamilton-Gleichungen |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005426803&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT kuksinsergejb nearlyintegrableinfinitedimensionalhamiltoniansystems |