This book is concerned with the bifurcation theory, the study of the changes in the structures of the solution of ordinary differential equations as parameters of the model vary. The theory has developed rapidly over the past two decades. Chapters 1 and 2 of the book introduce two systematic methods of simplifying equations: centre manifold theory and normal form theory, by which the dimension of equations may be reduced and the forms changed so that they are as simple as possible. Chapters 3-5 of the book study in considerable detail the bifurcation of those one- or two-dimensional equations with one, two or several parameters. This book is aimed at mathematicians and graduate students interested in dynamical systems, ordinary differential equations and/or bifurcation theory. The basic knowledge required by this book is advanced calculus, functional analysis and qualitative theory of ordinary differential equations.
Preface; 1. Center manifolds; 2. Normal forms; 3. Codimension one bifurcations; 4. Codimension two bifurcations; 5. Bifurcations with codimension higher that two; Bibliography; Index.
Reviews for Normal Forms and Bifurcation of Planar Vector Fields
I cordially recommend the book to researchers new to this field. Henk Broer, Bulletin of the American Mathematical Society This book is clearly written, replete with biographical notes, and careful in its rigor. It is a must for anyone interested in ordinary differential equations of bifurcation theory. Kennneth R. Meyer, SIAM Review ...The presentation in the book enters into fine detail and is rather complete... Mathematical Reviews