Normal Forms and Bifurcation of Planar Vector Fields

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Paperback | 8 January 2009

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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 3â"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.

Industry Reviews

"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

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Non-Fiction Mathematics Calculus & Mathematical Analysis Differential Calculus & Equations Geometry Differential & Riemannian Geometry

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Hardcover

Published: 7th November 1994

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Preface
Center manifolds
Normal forms
Codimension one bifurcations
Codimension two bifurcations
Bifurcations with codimension higher that two
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

Normal Forms and Bifurcation of Planar Vector Fields

At a Glance

Paperback

Industry Reviews

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How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Hardcover

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