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arXiv 0810.52822008-10-29math.DS

平面解析向量场鲁棒normal forms的自动计算

Automated computation of robust normal forms of planar analytic vector fields

Tomas Johnson, Warwick Tucker

发表信息：: Discrete and continuous dynamical systems - Series B 12(4):769-782 (2009).
DOI：: 10.3934/dcdsb.2009.12.769

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摘要：

我们构造了一个自动验证算法，计算一个接近身份的变量变量变换，使一般的鞍点到一个正常的形式。该变换在基础向量场中是鲁棒的，并且在鞍点的可计算邻域上是解析的。规范形式适用于计算鞍点附近的流动，以及轨迹通过鞍点所需的时间。几个例子说明了这种方法的有效性。

英文摘要：

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.

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