Automated computation of robust normal forms of planar analytic vector fields
2009 (English)In: Discrete and continuous dynamical systems. Series B, ISSN 1531-3492, Vol. 12, no 4, 769-782 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2009. Vol. 12, no 4, 769-782 p.
Normal Forms, Hyperbolic fixed points, Numerical integration
IdentifiersURN: urn:nbn:se:uu:diva-103152DOI: 10.3934/dcdsb.2009.12.769ISI: 000271091400005OAI: oai:DiVA.org:uu-103152DiVA: diva2:217593