Methods of Bifurcation Theory

CHOW, Shui-Nee / HALE, Jack K,

ISBN 10: 0387906649 / ISBN 13: 9780387906645

Published by Springer Verlag, New York, 1982

About this Item

97 Ill. (Grundlehren der mathematischen Wissenschaften ; 251).

Seller Inventory # DSY-0393

Bibliographic Details

• Title: Methods of Bifurcation Theory
• Publisher: Springer Verlag, New York
• Publication Date: 1982
• Language: English
• ISBN 10: 0387906649
• ISBN 13: 9780387906645
• Binding: Hardcover
• Edition: 1st Edition
• Condition: Good
• Seller catalogs:
  • Mathematik / Mathematics

About this title

Synopsis

An alternative title for this book would perhaps be Nonlinear Analysis, Bifurcation Theory and Differential Equations. Our primary objective is to discuss those aspects of bifurcation theory which are particularly meaningful to differential equations. To accomplish this objective and to make the book accessible to a wider we have presented in detail much of the relevant background audience, material from nonlinear functional analysis and the qualitative theory of differential equations. Since there is no good reference for some of the mate- rial, its inclusion seemed necessary. Two distinct aspects of bifurcation theory are discussed-static and dynamic. Static bifurcation theory is concerned with the changes that occur in the structure of the set of zeros of a function as parameters in the function are varied. If the function is a gradient, then variational techniques play an important role and can be employed effectively even for global problems. If the function is not a gradient or if more detailed information is desired, the general theory is usually local. At the same time, the theory is constructive and valid when several independent parameters appear in the function. In differential equations, the equilibrium solutions are the zeros of the vector field. Therefore, methods in static bifurcation theory are directly applicable.

Synopsis

The author's primary objective in this book is to discuss those aspects of bifurcation theory which are particularly meaningful to differential equations. To acccomplish this objective and to make the book accessible to a wider audience, much of the relevant background material from nonlinear functional analysis and the qualitative theory of differential equations is presented in detail. Two distinct aspects of bifurcation theory are discussed - static and dynamic. Static bifurcation theory is concerned with the changes that occur in the structure of the set of zeros of a function as parameters in the function are varied. Dynamic bifurcation theory is concerned with the changes that occur in the structure of the limit sets of solutions of differential equations as parameters in the vector field are varied. This second printing contains extensive corrections and revisions throughout the book.