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Applied Mathematical Sciences #0072: Mutiphase Averaging for Classical Systems: With Applications to Adiabatic Theorems

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Applied Mathematical Sciences #0072: Mutiphase Averaging for Classical Systems: With Applications to Adiabatic Theorems Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

This book presents work to clarify and render accessible the main results in averaging for ODE's since the appearance of Bogoliubov and Mitropolski's book, and to give at the same time a survey of the adiabatic theorems which more or less readily follow from those results.

Table of Contents

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.

Product Details

ISBN:
9780387967783
Author:
Lochak, P.
Author:
Meunier, C.
Translator:
Dumas, H. S.
Author:
Dumas, H. S.
Publisher:
Springer
Location:
New York, NY
Subject:
Differential Equations
Subject:
Dynamics
Subject:
Average
Subject:
Averaging method (Differential equations)
Subject:
Adiabatic invariants.
Subject:
Averaging method
Subject:
Differential equations -- Asymptotic theory.
Subject:
Mathematical Analysis
Subject:
Analysis
Subject:
Mathematics-Differential Equations
Subject:
Mathematics
Subject:
Language, literature and biography
Subject:
mathematics and statistics
Subject:
Global analysis (Mathematics)
Copyright:
Edition Description:
Softcover reprint of the original 1st ed. 1988
Series:
Applied Mathematical Sciences
Series Volume:
5
Publication Date:
19880907
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
371
Dimensions:
235 x 155 mm 1160 gr

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Related Subjects

Health and Self-Help » Health and Medicine » General
Health and Self-Help » Health and Medicine » General Medicine
Science and Mathematics » Mathematics » Differential Equations
Science and Mathematics » Mathematics » Systems Theory
Science and Mathematics » Physics » Classical Mechanics

Applied Mathematical Sciences #0072: Mutiphase Averaging for Classical Systems: With Applications to Adiabatic Theorems New Trade Paper
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Product details 371 pages Springer-Verlag - English 9780387967783 Reviews:
"Synopsis" by , This book presents work to clarify and render accessible the main results in averaging for ODE's since the appearance of Bogoliubov and Mitropolski's book, and to give at the same time a survey of the adiabatic theorems which more or less readily follow from those results.
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