Mathematics-Dynamical Systems

Averaging Methods in Nonlinear Dynamical Systems

US$5.00 US$60.00

Title (user) : Averaging Methods in Nonlinear Dynamical SystemsTitle (google) : AvgMethodsNonlinearISBN : 0387962298,9780387962290DDC : 515.3/55LCC : QA1 .A647 vol. 59,QA372 .A647 vol. 59DOI : 10.1007/978-1-4757-4575-7GoogleBook ID :...
Description

Title (user) : Averaging Methods in Nonlinear Dynamical Systems

Title (google) : AvgMethodsNonlinear

ISBN : 0387962298,9780387962290

DDC : 515.3/55

LCC : QA1 .A647 vol. 59,QA372 .A647 vol. 59

DOI : 10.1007/978-1-4757-4575-7

GoogleBook ID : fZpV9vCYhjsC

OpenLibrary ID : OL2540878M

Edition : 1

Series : Applied Mathematical Sciences 59

Authors (user) : Jan A. Sanders, Ferdinand Verhulst (auth.)

Authors (google) : Jan Anton Sanders,Ferdinand Verhulst

Publisher : Springer New York

Language : English

Publication Date : 1985

Scanned : yes (300 DPI)

File Format : djvu

Categories : Education


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Description (user) :

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


------------------------------------------

Description (google) :
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 Averaging Methods in Nonlinear Dynamical Systems. 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. Book jacket.


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Table of contents :
Front Matter....Pages N2-x
Basic Material....Pages 1-8
Asymptotics of Slow-time Processes, First Steps....Pages 9-32
The Theory of Averaging....Pages 33-66
Attraction....Pages 67-82
Averaging over Spatial Variables: Systems with Slowly Varying Frequency and Passage through Resonance....Pages 83-123
Normal Forms....Pages 124-142
Hamiltonian Systems....Pages 143-179
Appendices....Pages 181-235
Back Matter....Pages 236-249

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