Title Averaging methods in nonlinear dynamical systems / J.A. Sanders, F. Verhulst and J. Murdock

Edition 2nd ed Published New York : Springer, ©2007

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Description 1 online resource (xxi, 431 pages) : illustrations Series Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 59 Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 59. 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 Bibliography Includes bibliographical references (pages 394-411) and indexes In Springer eBooks Subject Differential equations, Nonlinear -- Numerical solutions. Differentiable dynamical systems. Averaging method (Differential equations) Averaging method (Differential equations) Differential equations, Nonlinear -- Numerical solutions. Differentiable dynamical systems. Averaging method (Differential equations) Differentiable dynamical systems Differential equations, Nonlinear -- Numerical solutions Form Electronic book Author Verhulst, F. (Ferdinand), 1939- Murdock, James A ISBN 9780387489162 0387489169 9780387489186 0387489185 9786611066208 6611066209

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