Multiphase Averaging for Classical Systems: With Applications to Adiabatic Theorems
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1988
|
| Schriftenreihe: | Applied Mathematical Sciences
72 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In the past several decades many significant results in averaging for systems of ODE's have been obtained. These results have not attracted a tention in proportion to their importance, partly because they have been overshadowed by KAM theory, and partly because they remain widely scattered - and often untranslated - throughout the Russian literature. The present book seeks to remedy that situation by providing a summary, including proofs, of averaging and related techniques for single and multiphase systems of ODE's. The first part of the book surveys most of what is known in the general case and examines the role of ergodicity in averaging. Stronger stability results are then obtained for the special case of Hamiltonian systems, and the relation of these results to KAM Theory is discussed. Finally, in view of their close relation to averaging methods, both classical and quantum adiabatic theorems are considered at some length. With the inclusion of nine concise appendices, the book is very nearly self-contained, and should serve the needs of both physicists desiring an accessible summary of known results, and of mathematicians seeing an introduction to current areas of research in averaging |
| Beschreibung: | 1 Online-Ressource (XI, 360p. 60 illus) |
| ISBN: | 9781461210443 9780387967783 |
| ISSN: | 0066-5452 |
| DOI: | 10.1007/978-1-4612-1044-3 |
Internformat
MARC
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| 500 | |a In the past several decades many significant results in averaging for systems of ODE's have been obtained. These results have not attracted a tention in proportion to their importance, partly because they have been overshadowed by KAM theory, and partly because they remain widely scattered - and often untranslated - throughout the Russian literature. The present book seeks to remedy that situation by providing a summary, including proofs, of averaging and related techniques for single and multiphase systems of ODE's. The first part of the book surveys most of what is known in the general case and examines the role of ergodicity in averaging. Stronger stability results are then obtained for the special case of Hamiltonian systems, and the relation of these results to KAM Theory is discussed. Finally, in view of their close relation to averaging methods, both classical and quantum adiabatic theorems are considered at some length. With the inclusion of nine concise appendices, the book is very nearly self-contained, and should serve the needs of both physicists desiring an accessible summary of known results, and of mathematicians seeing an introduction to current areas of research in averaging | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Lochak, Pierre 1957- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-1044-3 |
| format | Electronic eBook |
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| id | DE-604.BV042419723 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:05Z |
| institution | BVB |
| isbn | 9781461210443 9780387967783 |
| issn | 0066-5452 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027855140 |
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| physical | 1 Online-Ressource (XI, 360p. 60 illus) |
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| publishDate | 1988 |
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| spelling | Lochak, Pierre 1957- Verfasser (DE-588)1072789507 aut Multiphase Averaging for Classical Systems With Applications to Adiabatic Theorems by Pierre Lochak, Claude Meunier New York, NY Springer New York 1988 1 Online-Ressource (XI, 360p. 60 illus) txt rdacontent c rdamedia cr rdacarrier Applied Mathematical Sciences 72 0066-5452 In the past several decades many significant results in averaging for systems of ODE's have been obtained. These results have not attracted a tention in proportion to their importance, partly because they have been overshadowed by KAM theory, and partly because they remain widely scattered - and often untranslated - throughout the Russian literature. The present book seeks to remedy that situation by providing a summary, including proofs, of averaging and related techniques for single and multiphase systems of ODE's. The first part of the book surveys most of what is known in the general case and examines the role of ergodicity in averaging. Stronger stability results are then obtained for the special case of Hamiltonian systems, and the relation of these results to KAM Theory is discussed. Finally, in view of their close relation to averaging methods, both classical and quantum adiabatic theorems are considered at some length. With the inclusion of nine concise appendices, the book is very nearly self-contained, and should serve the needs of both physicists desiring an accessible summary of known results, and of mathematicians seeing an introduction to current areas of research in averaging Mathematics Global analysis (Mathematics) Analysis Mathematik Mittelungsverfahren (DE-588)4126019-3 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Adiabatensatz (DE-588)4204479-0 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Asymptotische Methode (DE-588)4287476-2 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 s Mittelungsverfahren (DE-588)4126019-3 s 1\p DE-604 Differentialgleichung (DE-588)4012249-9 s Asymptotische Methode (DE-588)4287476-2 s 2\p DE-604 Adiabatensatz (DE-588)4204479-0 s 3\p DE-604 Meunier, Claude Sonstige oth https://doi.org/10.1007/978-1-4612-1044-3 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lochak, Pierre 1957- Multiphase Averaging for Classical Systems With Applications to Adiabatic Theorems Mathematics Global analysis (Mathematics) Analysis Mathematik Mittelungsverfahren (DE-588)4126019-3 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Adiabatensatz (DE-588)4204479-0 gnd Differentialgleichung (DE-588)4012249-9 gnd Asymptotische Methode (DE-588)4287476-2 gnd |
| subject_GND | (DE-588)4126019-3 (DE-588)4020929-5 (DE-588)4204479-0 (DE-588)4012249-9 (DE-588)4287476-2 |
| title | Multiphase Averaging for Classical Systems With Applications to Adiabatic Theorems |
| title_auth | Multiphase Averaging for Classical Systems With Applications to Adiabatic Theorems |
| title_exact_search | Multiphase Averaging for Classical Systems With Applications to Adiabatic Theorems |
| title_full | Multiphase Averaging for Classical Systems With Applications to Adiabatic Theorems by Pierre Lochak, Claude Meunier |
| title_fullStr | Multiphase Averaging for Classical Systems With Applications to Adiabatic Theorems by Pierre Lochak, Claude Meunier |
| title_full_unstemmed | Multiphase Averaging for Classical Systems With Applications to Adiabatic Theorems by Pierre Lochak, Claude Meunier |
| title_short | Multiphase Averaging for Classical Systems |
| title_sort | multiphase averaging for classical systems with applications to adiabatic theorems |
| title_sub | With Applications to Adiabatic Theorems |
| topic | Mathematics Global analysis (Mathematics) Analysis Mathematik Mittelungsverfahren (DE-588)4126019-3 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Adiabatensatz (DE-588)4204479-0 gnd Differentialgleichung (DE-588)4012249-9 gnd Asymptotische Methode (DE-588)4287476-2 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Mathematik Mittelungsverfahren Gewöhnliche Differentialgleichung Adiabatensatz Differentialgleichung Asymptotische Methode |
| url | https://doi.org/10.1007/978-1-4612-1044-3 |
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