Series 
Applied mathematical sciences (SpringerVerlag New York Inc.) ; v. 59. 

Applied mathematical sciences (SpringerVerlag 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 394411) 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 (FirstLevel) Normal Form Theory  Nilpotent (Classical) Normal Form  HigherLevel Normal Form Theory  The History of the Theory of Averaging  A 4Dimensional 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 

0387489169 

9780387489186 (eISBN) 

0387489185 (eISBN) 

9786611066208 

6611066209 
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. 
