© 2015

Bifurcation without Parameters

  • This is the first systematic treatment of the topic

  • Numerous figures augment the analytic treatment and assist in understanding

  • The abstract theory is complemented by many applications


Part of the Lecture Notes in Mathematics book series (LNM, volume 2117)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Preliminaries

    1. Front Matter
      Pages 1-1
    2. Stefan Liebscher
      Pages 3-12
    3. Stefan Liebscher
      Pages 13-19
    4. Stefan Liebscher
      Pages 21-23
  3. Codimension One

    1. Front Matter
      Pages 25-25
    2. Stefan Liebscher
      Pages 27-34
    3. Stefan Liebscher
      Pages 35-41
    4. Stefan Liebscher
      Pages 43-47
  4. Codimension Two

    1. Front Matter
      Pages 55-55
    2. Stefan Liebscher
      Pages 57-65
    3. Stefan Liebscher
      Pages 67-79
    4. Stefan Liebscher
      Pages 81-102
    5. Stefan Liebscher
      Pages 103-108
    6. Stefan Liebscher
      Pages 109-113
  5. Beyond Codimension Two

    1. Front Matter
      Pages 129-129
    2. Stefan Liebscher
      Pages 131-133

About this book


Targeted at mathematicians having at least a basic familiarity with classical bifurcation theory, this monograph provides a systematic classification and analysis of bifurcations without parameters in dynamical systems. Although the methods and concepts are briefly introduced, a prior knowledge of center-manifold reductions and normal-form calculations will help the reader to appreciate the presentation. Bifurcations without parameters occur along manifolds of equilibria, at points where normal hyperbolicity of the manifold is violated. The general theory, illustrated by many applications, aims at a geometric understanding of the local dynamics near the bifurcation points.


34C23,34C20,34C37,37G99,35B32 Bifurcation without parameters Equilibria Manifolds Nonlinear dynamical systems ordinary differential equations

Authors and affiliations

  1. 1.Institur für MathematikFreie Universität BerlinBerlinGermany

Bibliographic information