Bifurcations of limit cycles in coupled networks of Hamiltonian systems

Guillaume Cantin (1)

1 LMAH - Laboratoire de Mathématiques Appliquées du Havre

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.

Mots clés: Hamiltonian system; limit cycle; perturbation; Melnikov function; bifurcation

Domaines: Mathématiques [math]

Guillaume Cantin. Bifurcations of limit cycles in coupled networks of Hamiltonian systems. 2018. ⟨hal-01673572⟩