November  2009, 12(4): 769-782. doi: 10.3934/dcdsb.2009.12.769

Automated computation of robust normal forms of planar analytic vector fields

1. 

Department of Mathematics, Uppsala University, BOX 480, 751 06 Uppsala, Sweden

2. 

Department of Mathematics, University of Bergen, Johannes Brunsgate 12, 5008 Bergen, Norway

Received  October 2008 Revised  April 2009 Published  August 2009

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.
Citation: Tomas Johnson, Warwick Tucker. Automated computation of robust normal forms of planar analytic vector fields. Discrete & Continuous Dynamical Systems - B, 2009, 12 (4) : 769-782. doi: 10.3934/dcdsb.2009.12.769
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