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 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.
Original language | English |
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Pages (from-to) | 769-782 |
Number of pages | 14 |
Journal | Discrete and Continuous Dynamical Systems - Series B |
Volume | 12 |
Issue number | 4 |
DOIs | |
Publication status | Published - 1 Nov 2009 |
Externally published | Yes |
Keywords
- Hyperbolic fixed points
- Normal forms
- Numerical integration