Automated computation of robust normal forms of planar analytic vector fields

• 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.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

Normal Forms

Hyperbolic fixed points

Numerical integration

MATHEMATICS

MATEMATIK

Publication and Content Type

ref (subject category)

art (subject category)