Automated computation of robust normal forms of planar analytic vector fields

Tomas Johnson; Warwick Tucker

doi:10.3934/dcdsb.2009.12.769

Automated computation of robust normal forms of planar analytic vector fields

Tomas Johnson, Warwick Tucker

Research output: Contribution to journal › Article › Research › peer-review

5 Citations (Scopus)

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
Pages (from-to)	769-782
Number of pages	14
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	12
Issue number	4
DOIs	https://doi.org/10.3934/dcdsb.2009.12.769
Publication status	Published - 1 Nov 2009
Externally published	Yes

Keywords

Hyperbolic fixed points
Normal forms
Numerical integration

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10.3934/dcdsb.2009.12.769

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Automated computation of robust normal forms of planar analytic vector fields

Abstract

Keywords

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