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  • © 2007

Attractivity and Bifurcation for Nonautonomous Dynamical Systems

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

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Table of contents (7 chapters)

  1. Front Matter

    Pages IX-XI
  2. Introduction

    Pages 1-6
  3. LinearSystems

    Pages 81-113
  4. Nonlinear Systems

    Pages 115-135
  5. Back Matter

    Pages 193-215

About this book

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
  • ordinary differential equations

Reviews

From the reviews:

"In this volume the reader will find a theory of breakdown of stability and a theory of transition for a one-parameter family of nonautonomous dynamical systems. … This book presents a wealth of interesting theoretical concepts, which will certainly be important in the further development of the theory of breakdown of stability and of transition for nonautonomous dynamical systems." (Russell A. Johnson, Mathematical Reviews, Issue 2008 k)

Authors and Affiliations

  • Lehrstuhl für Angewandte Analysis, Universität Augsburg, Augsburg, Germany

    Martin Rasmussen

Bibliographic Information

  • Book Title: Attractivity and Bifurcation for Nonautonomous Dynamical Systems

  • Authors: Martin Rasmussen

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-540-71225-1

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2007

  • Softcover ISBN: 978-3-540-71224-4Published: 08 June 2007

  • eBook ISBN: 978-3-540-71225-1Published: 26 May 2007

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XI, 217

  • Topics: Differential Equations, Dynamical Systems

Buying options

eBook USD 39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions