Overview
- Authors:
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Pierre Lochak
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Centre de Mathematiques, Ecole Normale Superieure, Paris Cedex 05, France
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Claude Meunier
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Centre de Physique Theorique, Ecole Polytechnique, Palaiseau Cedex, France
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Table of contents (10 chapters)
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- Pierre Lochak, Claude Meunier
Pages 1-9
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- Pierre Lochak, Claude Meunier
Pages 11-24
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- Pierre Lochak, Claude Meunier
Pages 25-66
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- Pierre Lochak, Claude Meunier
Pages 67-116
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- Pierre Lochak, Claude Meunier
Pages 117-132
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- Pierre Lochak, Claude Meunier
Pages 133-152
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- Pierre Lochak, Claude Meunier
Pages 153-182
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- Pierre Lochak, Claude Meunier
Pages 183-227
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- Pierre Lochak, Claude Meunier
Pages 229-247
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- Pierre Lochak, Claude Meunier
Pages 249-268
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Back Matter
Pages 269-361
About this book
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.
Authors and Affiliations
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Centre de Mathematiques, Ecole Normale Superieure, Paris Cedex 05, France
Pierre Lochak
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Centre de Physique Theorique, Ecole Polytechnique, Palaiseau Cedex, France
Claude Meunier