A non-symplectic KAM phenomenon for singular holomorphic vector fields (Q2721627)
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scientific article; zbMATH DE number 1616345
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A non-symplectic KAM phenomenon for singular holomorphic vector fields |
scientific article; zbMATH DE number 1616345 |
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26 February 2002
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KAM theory
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holomorphic vector field
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holomorphic normal form
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Lie algebra
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0.9675747
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0.8950739
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0.8870166
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0.87252045
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0.8719691
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0.8718326
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A non-symplectic KAM phenomenon for singular holomorphic vector fields (English)
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The author performs an interesting investigation of the germs of holomorphic vector fields at the origin of \(\mathbb C^{n}\). If such a germ \(X\) is a perturbation of a singular completely integrable system and its linear part admits non-trivial polynomial first integrals, then it admits a lot of invariant analytic subsets in a neighbourhood of \(0\) and, despite the fact that \(X\) is not holomorphically normalizable, it has a holomorphic normal form in a neighbourhood of the origin. An open question is thus answered.
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