Configurations of zeroes of analytic functions (Q2748288)
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scientific article; zbMATH DE number 1659150
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Configurations of zeroes of analytic functions |
scientific article; zbMATH DE number 1659150 |
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Configurations of zeroes of analytic functions (English)
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2001
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analytic vector fields
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singular perturbations
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Melnikov method
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The author explores small perturbations of an analytic family of vector fields in the very delicate case of singular perturbation (the initial family is zero). First, the author reduces the study to the case of 1-parameter families by using the curve selection lemma for subanalytic sets, then completes it with the help of the Melnikov functions inspired by \textit{R. Roussarie} [Qual. Theory Dyn. Syst. 2, 67--78 (2001; Zbl 1081.37030)]. This is a very interesting paper.
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