Averaging Methods in Nonlinear Dynamical Systems
(Sprache: Englisch)
Perturbation theory and in particular normal form theory has shown strong growth in recent decades. This book is a revision of the first edition of the averaging book. Updated chapters represent new insights in averaging and offer an effective entrance into this topic.
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Produktinformationen zu „Averaging Methods in Nonlinear Dynamical Systems “
Perturbation theory and in particular normal form theory has shown strong growth in recent decades. This book is a revision of the first edition of the averaging book. Updated chapters represent new insights in averaging and offer an effective entrance into this topic.
Klappentext zu „Averaging Methods in Nonlinear Dynamical Systems “
Perturbation theory and in particular normal form theory has shown strong growth in recent decades. This book is a drastic revision of the first edition of the averaging book. The updated chapters represent new insights in averaging, in particular its relation with dynamical systems and the theory of normal forms. Also new are survey appendices on invariant manifolds. One of the most striking features of the book is the 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 illuminating diagrams.
Perturbation theory and in particular normal form theory has shown strong growth during the last decades. So it is not surprising that we are presenting a rather drastic revision of the first edition of the averaging book. The chapters have been updated and represent new insights in averaging, in particular its relation with dynamical systems and the theory of normal forms. Also new are survey appendices on invariant manifolds. Since the first edition, the book has expanded in length and the third author, James Murdock has been added.
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. Old proverb: one picture is worth a thousand words. The book includes an extensive bibliography and a detailed index. Format and printing are of the high standard common to Springer books. In conclusion, the authors completely achieve their goal and present their case in a concise manner. The book offers an effective entrance into a lively area of research and will be very valuable for those who study and do research in the field of asymptotic methods.
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. Old proverb: one picture is worth a thousand words. The book includes an extensive bibliography and a detailed index. Format and printing are of the high standard common to Springer books. In conclusion, the authors completely achieve their goal and present their case in a concise manner. The book offers an effective entrance into a lively area of research and will be very valuable for those who study and do research in the field of asymptotic methods.
Inhaltsverzeichnis zu „Averaging Methods in Nonlinear Dynamical Systems “
- Basic Material and Asymptotics- Averaging: the periodic case
- Methodology of Averaging
- Averaging: 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
- A The History of the Theory of Averaging
- B A 4-dimensional example of Hopf Bifurcation
- C Invariant manifolds by averaging
- D Celestial Mechanics
- E On averaging methods for partial differential equations
- Bibtex errors
- References.
Bibliographische Angaben
- Autoren: Jan A. Sanders , Ferdinand Verhulst , James Murdock
- 2007, 2nd ed., 434 Seiten, Maße: 16 x 24,1 cm, Kartoniert (TB), Englisch
- Verlag: Springer, New York
- ISBN-10: 0387489169
- ISBN-13: 9780387489162
- Erscheinungsdatum: 06.06.2007
Sprache:
Englisch
Rezension zu „Averaging Methods in Nonlinear Dynamical Systems “
From the reviews of the second edition:"This monograph is a second edition comprising a thorough revision and an expansion of the first one ... . Thus, the reader is exposed to the practice of examining both concrete applications ... and theory. ... comprehensive content is extremely well written. ... The presentation is self-contained, thus offering a high level and convenient exposition to those who wish to study the subject matter as a whole. ... The text introduces particular notations which are not too common in the literature." (Zvi Artstein, Mathematical Reviews, Issue 2008 h)"The new book will be an ideal place to learn about averaging, including what's new in the last quarter century ... . Overall, the authors are to be commended for writing this timely and important piece of scholarship, which should teach many about their topic and related analysis." (Robert E. O' Malley, Jr., Siam Review, Vol. 51 (1), 2009)"This monograph is a revised and expanded second edition of the original text from 1985 by the first two authors. This first edition has since then become one of the standard references for the modern theory of averaging and singular perturbations of ordinary differential equations. Without doubt the second edition will continue this legacy. ... The book is well-written with full proves and a wealth of enlightening examples. It can only be warmly recommended to everybody working in this field ... ." (G. Teschl, Monatshefte für Mathematik, Vol. 156 (4), April, 2009)
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