rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Multiphase Averaging for Classical Systems
    sub title: With Applications to Adiabatic Theorems
  name:
    name part: Lochak, P. (Pierre)
    role:
      role term: creator
  name:
    name part: Meunier, Claude.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: Electronic books.
  origin info:
    place:
      place term: nyu
    date issued: 1988
    issuance: monographic
  language:
    language term: eng
  physical description:
    reformatting quality: access
    form: remote
    extent: 1 online resource (xi, 360 pages 60 illustrations)
  abstract: 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.
  table of contents: Introduction and Notation -- Ergodicity -- On Frequency Systems and First Results for Two Frequency Systems -- Two Frequency Systems; Neistadt's Results -- N Frequency Systems; Neistadt's Result Based on Anosov's Method -- N Frequency Systems; Neistadt's Results Based on Kasuga's Method -- Hamiltonian Systems -- Adiabatic Theorems in One Dimension -- The Classical Adiabatic Theorems in Many Dimensions -- The Quantum Adiabatic Theorem -- Appendices -- Bibliography -- Bibliographical Notes -- Index.
  note: by Pierre Lochak, Claude Meunier.
  note: Electronic resource.
  subject:
    topic: Mathematics
  subject:
    topic: Global analysis (Mathematics)
  subject:
    topic: Global analysis (Mathematics)
  subject:
    topic: Mathematics
  classification: QA299.6-433
  classification: 515
  related item:
    title info:
      title: Applied mathematical sciences (Springer-Verlag New York Inc.) ; 72
  identifier: 9781461210443 (electronic bk.)
  identifier: 1461210445 (electronic bk.)
  identifier: 9780387967783
  identifier: 0387967788
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: AU@
    record creation date: 121227
    record change date: 20260422171159.9
    record identifier: in00003558548
    language of cataloging:
      language term: eng