Ordinary Differential Equations and Dynamical Systems

1. Front Matter

   Pages i-xi

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2. Introduction

   • Thomas C. Sideris

   Pages 1-3

3. Linear Systems

   • Thomas C. Sideris

   Pages 5-19

4. Existence Theory

   • Thomas C. Sideris

   Pages 21-51

5. Nonautonomous Linear Systems

   • Thomas C. Sideris

   Pages 53-72

6. Results from Functional Analysis

   • Thomas C. Sideris

   Pages 73-87

7. Dependence on Initial Conditions and Parameters

   • Thomas C. Sideris

   Pages 89-94

8. Linearization and Invariant Manifolds

   • Thomas C. Sideris

   Pages 95-118

9. Periodic Solutions

   • Thomas C. Sideris

   Pages 119-154

10. Center Manifolds and Bifurcation Theory

    • Thomas C. Sideris

    Pages 155-198

11. The Birkhoff Smale Homoclinic Theorem

    • Thomas C. Sideris

    Pages 199-217

12. Back Matter

    Pages 219-225

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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 presentation emphasizes commonly used techniques without necessarily striving for completeness or for the treatment of a large number of topics. 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 stability of periodic solutions, bifurcations, normal forms, and the existence of transverse homoclinic points and their link to chaotic dynamics. A common thread throughout the second part is the use of the implicit function theorem in Banach space. Chapter 5, devoted to this topic, the serves as the bridge between the two halves of the book.

• dynamical systems
• implicit function theorem
• ordinary differential equations

From the book reviews:

“This is a very nice text for a beginners course on ordinary differential equations and dynamical systems. … All basic results about ordinary differential equations are present. … Each chapter contains examples and exercises … . this book will certainly be an excellent reference text.” (Santiago Ibáñez, Mathematical Reviews, December, 2014)

• Department of Mathematics, University of California, Santa Barbara, USA

  Thomas C. Sideris

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