Normal Forms and Bifurcation of Planar Vector Fields [Hardcover]

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.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.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.This book is mainly concerned with the bifurcation theory of ODEs. Chapters 1 and 2 of the book introduce two systematic methods of simplifying equations: center manifold theory and normal form theory, by which one may reduce the dimension of equations and change forms of equations to be 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.Preface; 1. Center manifolds; 2. Normal forms; 3. Codimension one bifurcations; 4. Codimension two bifurcations; 5. Bifurcations with codimension higher that two; Bibliography; Index. 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