Bifurcations de Poincaré-Hopf dégénérées pour une famille de \(R^ 2\)-endomorphismes a deux paramètres. (Degenerate Poincaré-Hopf bifurcations of a two-parameter family of \({\mathbb{R}}^ 2\)-endomorphisms) (Q1084728)
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scientific article; zbMATH DE number 3980084
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Bifurcations de Poincaré-Hopf dégénérées pour une famille de \(R^ 2\)-endomorphismes a deux paramètres. (Degenerate Poincaré-Hopf bifurcations of a two-parameter family of \({\mathbb{R}}^ 2\)-endomorphisms) |
scientific article; zbMATH DE number 3980084 |
Statements
Bifurcations de Poincaré-Hopf dégénérées pour une famille de \(R^ 2\)-endomorphismes a deux paramètres. (Degenerate Poincaré-Hopf bifurcations of a two-parameter family of \({\mathbb{R}}^ 2\)-endomorphisms) (English)
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1986
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The authors study the degenerate Poincaré-Hopf bifurcation of a two- parameter family of transformations of the plane. They prove that for each resonance k there is at most one cycle in a neighborhood of a bifurcating fixed point. They construct analytically the solutions for the resonances \(k=1,2,3,4\), the case \(k=4\) being dealt with by an extension of an asymptotic method of Puiseux.
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endomorphism of the plane
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cycle
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degenerate Poincaré-Hopf bifurcation
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two-parameter family of transformations
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resonance
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bifurcating fixed point
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asymptotic method
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0.7894534468650818
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