The word bifurcation means division into two and is used in a wide sense to indicate every qualitative topological metamorphosis of a picture under the variation of parameters on which the object being studied depends. The objects can be diverse: for example, real or complex curves or surfaces, functions or mappings, manifolds or fiber bundles, vector fields or equations, differential or integral.


Vector Field Singular Point Phase Portrait Elliptic Curve Bifurcation Diagram 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1988

Authors and Affiliations

  • V. I. Arnold
    • 1
  1. 1.Steklov Mathematical InstituteMoscow GSP-1USSR

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