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Nonautonomous Bifurcation Theory

Concepts and Tools

  • Book
  • © 2023

Overview

Authors:
  1. Vasso Anagnostopoulou

    1. Department of Primary Care and Public Health, Brighton & Sussex Medical School, University of Sussex, Brighton, UK

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  2. Christian Pötzsche

    1. Institut für Mathematik, University of Klagenfurt, Klagenfurt, Austria

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    You can also search for this author in PubMed   Google Scholar

  3. Martin Rasmussen

    1. Department of Mathematics, Imperial College London, London, UK

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  • Gives a unique survey of different approaches to nonautonomous bifurcation theory
  • Examples guide the discussion and comparison of different approaches
  • Provides a unique collection of tools from the theory of nonautonomous dynamical systems

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction

    • Vasso Anagnostopoulou, Christian Pötzsche, Martin Rasmussen
    Pages 1-21

  3. Nonautonomous Differential Equations

    1. Front Matter

      Pages 23-24
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    2. Spectral Theory, Stability and Continuation

      • Vasso Anagnostopoulou, Christian Pötzsche, Martin Rasmussen
      Pages 25-39

    3. Nonautonomous Bifurcation

      • Vasso Anagnostopoulou, Christian Pötzsche, Martin Rasmussen
      Pages 41-63

    4. Reduction Techniques

      • Vasso Anagnostopoulou, Christian Pötzsche, Martin Rasmussen
      Pages 65-73

  4. Nonautonomous Difference Equations

    1. Front Matter

      Pages 75-77
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    2. Spectral Theory, Stability and Continuation

      • Vasso Anagnostopoulou, Christian Pötzsche, Martin Rasmussen
      Pages 79-94

    3. Nonautonomous Bifurcation

      • Vasso Anagnostopoulou, Christian Pötzsche, Martin Rasmussen
      Pages 95-115

    4. Reduction Techniques

      • Vasso Anagnostopoulou, Christian Pötzsche, Martin Rasmussen
      Pages 117-123

  5. Back Matter

    Pages 125-156
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Keywords

About this book

Bifurcation theory is a major topic in dynamical systems theory with profound applications. However, in contrast to autonomous dynamical systems, it is not clear what a bifurcation of a nonautonomous dynamical system actually is, and so far, various different approaches to describe qualitative changes have been suggested in the literature. The aim of this book is to provide a concise survey of the area and equip the reader with suitable tools to tackle nonautonomous problems. A review, discussion and comparison of several concepts of bifurcation is provided, and these are formulated in a unified notation and illustrated by means of comprehensible examples. Additionally, certain relevant tools needed in a corresponding analysis are presented.

Authors and Affiliations

  • Department of Primary Care and Public Health, Brighton & Sussex Medical School, University of Sussex, Brighton, UK

    Vasso Anagnostopoulou

  • Institut für Mathematik, University of Klagenfurt, Klagenfurt, Austria

    Christian Pötzsche

  • Department of Mathematics, Imperial College London, London, UK

    Martin Rasmussen

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