Double tangent extension method and first integrals (Q2865488)
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scientific article; zbMATH DE number 6234834
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Double tangent extension method and first integrals |
scientific article; zbMATH DE number 6234834 |
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Double tangent extension method and first integrals (English)
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29 November 2013
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first integrals
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integrable system
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Darboux point
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differential Galois theory
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The author presents a new method for the construction of first integrals of holomorphic vector fields. The basic idea is to differentiate the given first-order ordinary differential equation and to consider the obtained second-order equation as Newtonian equations of motion, as for the latter one methods from differential Galois theory can be used. As an application, vector fields whose entries are homogeneous polynomials are studied. A detailed discussion of the planar case is given and in higher dimensions some new examples of integrable systems are presented.
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0.7616919875144958
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