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.
|Number of pages||14|
|Journal||Discrete and Continuous Dynamical Systems - Series B|
|Publication status||Published - 1 Nov 2009|
- Hyperbolic fixed points
- Normal forms
- Numerical integration