On the bifurcations of a Hamiltonian having three homoclinic loops under \(\mathbb Z_{3}\) invariant quintic perturbations (Q2641551)
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scientific article
| Language | Label | Description | Also known as |
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| English | On the bifurcations of a Hamiltonian having three homoclinic loops under \(\mathbb Z_{3}\) invariant quintic perturbations |
scientific article |
Statements
On the bifurcations of a Hamiltonian having three homoclinic loops under \(\mathbb Z_{3}\) invariant quintic perturbations (English)
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20 August 2007
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The authors consider a planar autonomous system of differential equations which is obtained from a system with cubic Hamiltonian right-hand sides by adding small \(\mathbb Z_3\)-invariant quintic polynomials. It is assumed that the initial system has three homoclinic loops. The number and distribution of the appearing limit cycles are characterized.
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homoclinic loop bifurcation
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heteroclinic loop bifurcation
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Hopf bifurcation
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stability
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limit cycles
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