Multiphase Averaging for Classical Systems

With Applications to Adiabatic Theorems

  • Pierre Lochak
  • Claude Meunier

Part of the Applied Mathematical Sciences book series (AMS, volume 72)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Pierre Lochak, Claude Meunier
    Pages 1-9
  3. Pierre Lochak, Claude Meunier
    Pages 11-24
  4. Pierre Lochak, Claude Meunier
    Pages 25-66
  5. Pierre Lochak, Claude Meunier
    Pages 67-116
  6. Pierre Lochak, Claude Meunier
    Pages 117-132
  7. Pierre Lochak, Claude Meunier
    Pages 133-152
  8. Pierre Lochak, Claude Meunier
    Pages 153-182
  9. Pierre Lochak, Claude Meunier
    Pages 183-227
  10. Pierre Lochak, Claude Meunier
    Pages 229-247
  11. Pierre Lochak, Claude Meunier
    Pages 249-268
  12. Back Matter
    Pages 269-361

About this book

Introduction

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.

Keywords

Fourier series KAM theory Kolmogorov–Arnold–Moser theorem hamiltonian system integrable system maximum stability

Authors and affiliations

  • Pierre Lochak
    • 1
  • Claude Meunier
    • 2
  1. 1.Centre de MathematiquesEcole Normale SuperieureParis Cedex 05France
  2. 2.Centre de Physique TheoriqueEcole PolytechniquePalaiseau CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1044-3
  • Copyright Information Springer-Verlag New York Inc. 1988
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-96778-3
  • Online ISBN 978-1-4612-1044-3
  • Series Print ISSN 0066-5452
  • About this book