Bifurcations of limit cycles in coupled Hamiltonian systems

Abstract : This paper is devoted to the analysis of bifurcations of limit cycles in planar polynomial near-Hamiltonian systems. It is motivated by the second part of the sixteenth Hilbert's problem. We introduce a class of Hamiltonian systems which admit a high number of non-degenerate centers that can be arbitrarily located in the plane. We study several perturbations of those Hamiltonian systems, and analyze their effect by using the Melnikov method. One of those perturbations is defined along the gradient of the initial Hamiltonian. Finally, we demonstrate a new lower bound for the Hilbert number $H(n)$, which is of order $O(n^2 \sqrt{n})$ .
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Pré-publication, Document de travail
2018
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https://hal.archives-ouvertes.fr/hal-01673572
Contributeur : Guillaume Cantin <>
Soumis le : jeudi 1 février 2018 - 18:45:25
Dernière modification le : mercredi 7 février 2018 - 01:22:01

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  • HAL Id : hal-01673572, version 2

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Guillaume Cantin. Bifurcations of limit cycles in coupled Hamiltonian systems. 2018. 〈hal-01673572v2〉

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