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© 2013

Ordinary Differential Equations and Dynamical Systems

Book

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

  1. 1.Department of MathematicsUniversity of CaliforniaSanta BarbaraUSA

Bibliographic information

  • Book Title Ordinary Differential Equations and Dynamical Systems
  • Authors Thomas C. Sideris
  • Series Title Atlantis Studies in Differential Equations
  • Series Abbreviated Title Atlantis Studies in Differential Equations
  • 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 Mathematics and Statistics (R0)
  • Hardcover ISBN 978-94-6239-020-1
  • eBook ISBN 978-94-6239-021-8
  • Series ISSN 2214-6253
  • Series E-ISSN 2214-6261
  • Edition Number 1
  • Number of Pages XI, 225
  • Number of Illustrations 11 b/w illustrations, 0 illustrations in colour
  • Topics Ordinary Differential Equations
  • Buy this book on publisher's site

Reviews

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)