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arXiv · 0810.5282

Automated computation of robust normal forms of planar analytic vector fields

Tomas Johnson·Warwick Tucker
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Abstract

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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Tomas Johnson, Warwick Tucker. 2008-10-29. Automated computation of robust normal forms of planar analytic vector fields. https://doi.org/10.3934/dcdsb.2009.12.769

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