Automated computation of robust normal forms of planar analytic vector fields
- Resource Type
- Working Paper
- Authors
- Johnson, Tomas; Tucker, Warwick
- Source
- Discrete and continuous dynamical systems - Series B 12(4):769-782 (2009).
- Subject
- Mathematics - Dynamical Systems
34C20, 37M99, 65G20, 65L70
- Language
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.