Bifurcation of a class of planar non-Hamiltonian integrable systems with one center and one homoclinic loop (Q1604602)
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scientific article; zbMATH DE number 1764680
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Bifurcation of a class of planar non-Hamiltonian integrable systems with one center and one homoclinic loop |
scientific article; zbMATH DE number 1764680 |
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Bifurcation of a class of planar non-Hamiltonian integrable systems with one center and one homoclinic loop (English)
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8 July 2002
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The Hilbert 16th problem is still open even for quadratic Hamiltonian systems with quadratic perturbations. Under some conditions, the authors establish bifurcation results for the following system \[ x'=-y +a x^2 +b y^2 +\delta(\nu_1 x+ \nu_2 x y), \qquad y'=x(1+ c y) +\delta \nu_3 x^2, \] with the numerical parameters \(a,b,c, \delta, \nu_k\), \(k=1,2,3\).
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bifurcation
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Hilbert 16th problem
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Hamiltonian system
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quadratic perturbation
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