Geodesic
Limit Cycles of a Perturbation of a Polynomial Hamiltonian Systems of Degree 4 Symmetric with Respect to the Origin
Canadian mathematical bulletin, Tome 63 (2020) no. 3, pp. 547-561

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DOI

We study the number of limit cycles bifurcating from the origin of a Hamiltonian system of degree 4. We prove, using the averaging theory of order 7, that there are quartic polynomial systems close these Hamiltonian systems having 3 limit cycles.
DOI : 10.4153/S0008439519000626
Mots-clés : Hamiltonian system, linear type center, quartic polynomial, polynomial vector field, phase portrait 
Llibre, Jaume; Martínez, Paulina; Vidal, Claudio. Limit Cycles of a Perturbation of a Polynomial Hamiltonian Systems of Degree 4 Symmetric with Respect to the Origin. Canadian mathematical bulletin, Tome 63 (2020) no. 3, pp. 547-561. doi: 10.4153/S0008439519000626
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     author = {Llibre, Jaume and Mart{\'\i}nez, Paulina and Vidal, Claudio},
     title = {Limit {Cycles} of a {Perturbation} of a {Polynomial} {Hamiltonian} {Systems} of {Degree} 4 {Symmetric} with {Respect} to the {Origin}},
     journal = {Canadian mathematical bulletin},
     pages = {547--561},
     year = {2020},
     volume = {63},
     number = {3},
     doi = {10.4153/S0008439519000626},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439519000626/}
}
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