Bifurcations of infinite polycycles for polynomic vector fields on the plane (Q1894801)
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scientific article; zbMATH DE number 778923
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Bifurcations of infinite polycycles for polynomic vector fields on the plane |
scientific article; zbMATH DE number 778923 |
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Bifurcations of infinite polycycles for polynomic vector fields on the plane (English)
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12 February 1996
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The aim of the paper is to prove a particular case of a conjecture related to Hilbert's 16th problem. In fact, the author shows that under suitable conditions, for a parametrized family of sufficiently differentiable vector fields on the plane, hyperbolic 2-polycycles, which are different from resonant hyperbolic saddle points, are of finite cyclicity. This cyclicity is bounded by an integer which depends only on the order of nontriviality of the polycycle.
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polycycles
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Hilbert's 16th problem
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differentiable vector fields on the plane
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finite cyclicity
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