Ordinary Differential Equations and Dynamical Systems
This book is a mathematically rigorous introduction to the beautiful subject of ordinary differential equations for beginning graduate or advanced undergraduate students. Students should have a solid background in analysis and linear algebra. The presenta
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Thomas C. Sideris
Ordinary Differential Equations and Dynamical Systems
Atlantis Studies in Differential Equations Volume 2
Series Editor Michel Chipot, Zürich, Switzerland
For further volumes: www.atlantis-press.com
Aims and Scope of the Series The ‘‘Atlantis Studies in Differential Equations’’ publishes monographs in the area of differential equations, written by leading experts in the field and useful for both students and researchers. Books with a theoretical nature will be published alongside books emphasizing applications. For more information on this series and our other book series, please visit our website www.atlantis-press.com/publications/books AMSTERDAM – PARIS – BEIJING ATLANTIS PRESS Atlantis Press 29, avenue Laumière 75019 Paris, France
Thomas C. Sideris
Ordinary Differential Equations and Dynamical Systems
Thomas C. Sideris Department of Mathematics University of California Santa Barbara, CA USA
ISSN 2214-6253 ISBN 978-94-6239-020-1 DOI 10.2991/978-94-6239-021-8
ISSN 2214-6261 (electronic) ISBN 978-94-6239-021-8 (eBook)
Library of Congress Control Number: 2013947375 Ó Atlantis Press and the authors 2013 This book, or any parts thereof, may not be reproduced for commercial purposes in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system known or to be invented, without prior permission from the Publisher. Printed on acid-free paper
Dedicated to my father on the ocassion of his 90th birthday
Preface
Many years ago, I had my first opportunity to teach a graduate course on ordinary differential equations at UC, Santa Barbara. Not being a specialist, I sought advice and suggestions from others. In so doing, I had the good fortune of consulting with Manoussos Grillakis, who generously offered to share his lovely notes from John Mallet-Paret’s graduate course at Brown University. These notes, combined with some of my own home cooking and spiced with ingredients from other sources, evolved over numerous iterations into the current monograph. In publishing this work, my goal is to provide a mathematically rigorous introduction to the beautiful subject of ordinary differential equations to beginning graduate or advanced undergraduate students. I assume that students have a solid background in analysis and linear algebra. The presentation emphasizes commonly used techniques without necessarily striving for completeness or for the treatment of a large number of topics. I would half-jokingly subtitle this work as ‘‘ODE, as told by an analyst.’’ The first half of the book is devoted to the development of the basic theory: linear systems, existence and uniqueness of solutions to the initial value problem, flows, stability, and smooth dependence of solutions upon initial conditions and parameters. Much of this theory also serves as the paradigm for evolutionary partial differential equations. The second half of the book is devoted to geometric theory: topological conjugacy, invariant manifolds, existence and stabil
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