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Ordinary Differential Equations and Dynamical Systems

  • Thomas C.┬áSideris

Part of the Atlantis Studies in Differential Equations book series (ASDE, volume 2)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Thomas C. Sideris
    Pages 1-3
  3. Thomas C. Sideris
    Pages 5-19
  4. Thomas C. Sideris
    Pages 21-51
  5. Thomas C. Sideris
    Pages 53-72
  6. Thomas C. Sideris
    Pages 73-87
  7. Thomas C. Sideris
    Pages 89-94
  8. Thomas C. Sideris
    Pages 95-118
  9. Thomas C. Sideris
    Pages 119-154
  10. Thomas C. Sideris
    Pages 155-198
  11. Thomas C. Sideris
    Pages 199-217
  12. Back Matter
    Pages 219-225

About this book

Introduction

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.

Keywords

dynamical systems implicit function theorem ordinary differential equations

Authors and affiliations

  • Thomas C.┬áSideris
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaSanta BarbaraUSA

Bibliographic information

  • DOI https://doi.org/10.2991/978-94-6239-021-8
  • Copyright Information Atlantis Press and the authors 2013
  • Publisher Name Atlantis Press, Paris
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-94-6239-020-1
  • Online ISBN 978-94-6239-021-8
  • Series Print ISSN 2214-6253
  • Series Online ISSN 2214-6261
  • Buy this book on publisher's site