Automated computation of robust normal forms of planar analytic vector fields

Details Automated computation of robust normal forms of planar analytic vector fields Automated computation of robust normal forms of planar analytic vector fields

2008-10-29

arxiv.org/abs/0810.5282v1

Discrete and continuous dynamical systems - Series B 12(4):769-782 (2009).

Mathematics

Dynamical Systems

Scientific paper

10.3934/dcdsb.2009.12.769

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 neighborhood 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.

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