Attractivity and Bifurcation for Nonautonomous Dynamical Systems

  • Martin Rasmussen

Part of the Lecture Notes in Mathematics book series (LNM, volume 1907)

Table of contents

  1. Front Matter
    Pages IX-XI
  2. Pages 1-6
  3. Pages 81-113
  4. Pages 115-135
  5. Back Matter
    Pages 193-215

About this book

Introduction

Although, bifurcation theory of equations with autonomous and periodic time dependence is a major object of research in the study of dynamical systems since decades, the notion of a nonautonomous bifurcation is not yet established. In this book, two different approaches are developed which are based on special definitions of local attractivity and repulsivity. It is shown that these notions lead to nonautonomous Morse decompositions, which are useful to describe the global asymptotic behavior of systems on compact phase spaces. Furthermore, methods from the qualitative theory for linear and nonlinear systems are derived, and nonautonomous counterparts of the classical one-dimensional autonomous bifurcation patterns are developed.

Keywords

Nonautonomous dynamical system attractor and repeller theory bifurcation theory ordinary differential equation qualitative theory

Authors and affiliations

  • Martin Rasmussen
    • 1
  1. 1.Lehrstuhl für Angewandte AnalysisUniversität AugsburgAugsburgGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-71225-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 2007
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-71224-4
  • Online ISBN 978-3-540-71225-1
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book