Equivalence of nearly resonant planar saddles and Ecalle-Roussarie compensators (Q2782945)
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scientific article; zbMATH DE number 1725752
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Equivalence of nearly resonant planar saddles and Ecalle-Roussarie compensators |
scientific article; zbMATH DE number 1725752 |
Statements
8 April 2002
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resonant planar saddle
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equivalence of vector fields
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Ecalle-Roussarie compensators
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Dulac map
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Bogdanov-Takens bifurcation
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Equivalence of nearly resonant planar saddles and Ecalle-Roussarie compensators (English)
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The work is devoted to the calculation of a relationship between the special functions, which are called Ecalle-Roussarie compensators, and some asymptotic properties of equivalence with the linearized vector field. The Ecalle-Roussarie compensators are used extensively in the Dulac map of a family of planar vector fields in the neighbourhood of a nearly resonant saddle for the study of elementary graphics and of the Bogdanov-Takens bifurcation of planar diffeomorphisms. The changes of variables used by the authors are not smooth and they claim, at least for equivalencies, that they have much more information than just being \(C^1\).
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