Elementary Stability and Bifurcation Theory / Edition 2

by Gerard Iooss, Daniel D. Joseph

Overview

This substantially revised second edition teaches the bifurcation of asymptotic solutions to evolution problems governed by nonlinear differential equations. Written not just for mathematicians, it appeals to the widest audience of learners, including engineers, biologists, chemists, physicists and economists. For this reason, it uses only well-known methods of classical analysis at foundation level, while the applications and examples are specially chosen to be as varied as possible.

Product Details

ISBN-13:	9780387970684
Publisher:	Springer New York
Publication date:	12/06/1989
Series:	Undergraduate Texts in Mathematics Series
Edition description:	2nd rev. ed. 1990. Corr. 2nd printing 1997
Pages:	324
Product dimensions:	6.10(w) x 9.25(h) x 0.36(d)

Table of Contents

Asymptotic Solutions of Evolution Problems.- Bifurcation and Stability of Steady Solutions of Evolution Equations in One Dimension.- Imperfection Theory and Isolated Solutions Which Perturb Bifurcation.- Stability of Steady Solutions of Evolution Equations in Two Dimensions and n Dimensions. Appendices.- Bifurcation of Steady Solution in Two Dimensions and the Stability of the Bifurcating Solutions. Appendix.- Methods of Projection for General Problems of Bifurcation into Steady Solutions.- Bifurcation of Periodic Solutions from Steady Ones (Hopf Bifurcation) in Two Dimensions.- Bifurcation of Periodic Solutions in the General Case.- Subharmonic Bifurcation of Forced T-Periodic Solutions.- Bifurcation of Forced T-Periodic Solutions into Asymptotically Quasi-Periodic Solutions. Appendices.- Secondary Subharmonic and Symptotically Quasi-Periodic Bifurcation of Periodic Solutions (of Hopf's Type) in the Autonomous Case.- Stability and Bifurcation in Conservative Systems.

Editorial Reviews

(Advanced!) undergraduates and researchers with practical interest in the essentials and typical applications of bifurcation theory have for a decade been familiar with the first edition (1980) of this fine text. Drawing inspiration from Einstein's "everything should be made as simple as possible, but not simpler", the authors have undertaken simultaneously to simplify the treatment and to find room for discussion of some recent developments. Twelve chapters (many examples, many figures, no exercises) provide good coverage of the essentials of the asymptotics of (effectively) low-dimensional non- linear differential equations of evolution. Applications notable for their variety. Handsomely produced. (NW) Annotation c. Book News, Inc., Portland, OR (booknews.com)

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