Automated computation of robust normal forms of planar analytic vector fields

Tomas Johnson, Warwick Tucker

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5 Citations (Scopus)


We construct an auto-validated algorithm that calculates a close to identity change of variables which brings a general saddle point into a normal form. The transformation is robust in the underlying vector field, and is analytic on a computable neighbourhood of the saddle point. The normal form is suitable for computations aimed at enclosing the flow close to the saddle, and the time it takes a trajectory to pass it. Several examples illustrate the usefulness of this method.

Original languageEnglish
Pages (from-to)769-782
Number of pages14
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number4
Publication statusPublished - 1 Nov 2009
Externally publishedYes


  • Hyperbolic fixed points
  • Normal forms
  • Numerical integration

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