Stability of Nonautonomous Differential Equations

  • Luis Barreira
  • Claudia Valls
Part of the Lecture Notes in Mathematics book series (LNM, volume 1926)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Exponential dichotomies

  3. Stable manifolds and topological conjugacies

  4. Center manifolds, symmetry and reversibility

  5. Lyapunov regularity and stability theory

  6. Back Matter
    Pages 277-290

About this book

Introduction

Main theme of this volume is the stability of nonautonomous differential equations, with emphasis on the Lyapunov stability of solutions, the existence and smoothness of invariant manifolds, the construction and regularity of topological conjugacies, the study of center manifolds, as well as their reversibility and equivariance properties. Most results are obtained in the infinite-dimensional setting of Banach spaces. Furthermore, the linear variational equations are always assumed to possess a nonuniform exponential behavior, given either by the existence of a nonuniform exponential contraction or a nonuniform exponential dichotomy. The presentation is self-contained and has unified character. The volume contributes towards a rigorous mathematical foundation of the theory in the infinite-dimension setting, and may lead to further developments in the field. The exposition is directed to researchers as well as graduate students interested in differential equations and dynamical systems, particularly in stability theory.

Keywords

Lyapunov stability Stability theory center manifolds invariant manifolds nonuniform hyperbolicity topological conjugacies

Authors and affiliations

  • Luis Barreira
    • 1
  • Claudia Valls
    • 1
  1. 1.Instituto Superior Técnico1049-001LisboaPortugal

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-74775-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-74774-1
  • Online ISBN 978-3-540-74775-8
  • Series Print ISSN 0075-8434
  • About this book