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Author Sanders, J. A. (Jan A.)
Title Averaging methods in nonlinear dynamical systems / J.A. Sanders, F. Verhulst and J. Murdock.
Imprint New York : Springer, 2007.
Edition Second edition.

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Author Sanders, J. A. (Jan A.)
Series Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 59.
Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 59.
Subject Differential equations, Nonlinear -- Numerical solutions.
Differentiable dynamical systems.
Averaging method (Differential equations)
Alt Name Verhulst, F. (Ferdinand), 1939-
Murdock, James A.
Description 1 online resource (xxi, 431 pages) : illustrations.
Edition Second edition.
Bibliography Note Includes bibliographical references (pages 394-411) and indexes.
Contents Basic Material and Asymptotics -- Averaging: the Periodic Case -- Methodology of Averaging -- Averaging: the General Case -- Attraction -- Periodic Averaging and Hyperbolicity -- Averaging over Angles -- Passage Through Resonance -- From Averaging to Normal Forms -- Hamiltonian Normal Form Theory -- Classical (First-Level) Normal Form Theory -- Nilpotent (Classical) Normal Form -- Higher-Level Normal Form Theory -- The History of the Theory of Averaging -- A 4-Dimensional Example of Hopf Bifurcation -- Invariant Manifolds by Averaging -- Some Elementary Exercises in Celestial Mechanics -- On Averaging Methods for Partial Differential Equations.
Summary Perturbation theory and in particular normal form theory has shown strong growth during the last decades. So it is not surprising that the authors have presented an extensive revision of the first edition of the Averaging Methods in Nonlinear Dynamical Systems book. There are many changes, corrections and updates in chapters on Basic Material and Asymptotics, Averaging, and Attraction. Chapters on Periodic Averaging and Hyperbolicity, Classical (first level) Normal Form Theory, Nilpotent (classical) Normal Form, and Higher Level Normal Form Theory are entirely new and represent new insights in averaging, in particular its relation with dynamical systems and the theory of normal forms. Also new are surveys on invariant manifolds in Appendix C and averaging for PDEs in Appendix E. Since the first edition, the book has expanded in length and the third author, James Murdock has been added. Review of First Edition "One of the most striking features of the book is the nice collection of examples, which range from the very simple to some that are elaborate, realistic, and of considerable practical importance. Most of them are presented in careful detail and are illustrated with profuse, illuminating diagrams." - Mathematical Reviews.
ISBN 9780387489162
9780387489186 (e-ISBN)
0387489185 (e-ISBN)
OCLC # 191449138
Additional Format Print version: Sanders, J.A. (Jan A.). Averaging methods in nonlinear dynamical systems. 2nd ed. New York : Springer, 2007 9780387489162 0387489169 (DLC) 2007926028 (OCoLC)77012328.

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