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Articles, 2 records found

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12 p, 781.7 KB

Limit cycles of a perturbation of a polynomial Hamiltonian systems of degree 4 symmetric with respect to the origin / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Martínez, Y. Paulina (Universidad del Bío-Bío. Departamento de Matemática (Chile)) ; Vidal, Claudio (Universidad del Bío-Bío. Departamento de Matemática (Chile))
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.
2020 - DOI (Digital Object Identifier)

10.4153/S0008439519000626
Canadian mathematical bulletin, Vol. 63, Issue 3 (September 2020) , p. 547-561

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35 p, 913.1 KB

Phase portraits of linear type centers of polynomial hamiltonian systems with hamiltonian function of degree 5 of the form H = H1(x) + H2(y) / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Martínez, Y. Paulina (Universidad del Bío-Bío. Departamento de Matemática) ; Vidal, Claudio (Universidad del Bío-Bío. Departamento de Matemática)
We study the phase portraits on the Poincaré disc for all the linear type centers of polynomial Hamiltonian systems of degree 5 with Hamiltonian function H(x, y) = H + H, where H = 1/2 x + a/3 x + a/4 x + a/5 x and H = 1/2 y + b/3 y + b/4 y + b/5 y as function of the six real parameters a, a, a, b, b and b with ab ≠ 0. [...]
2019 - DOI (Digital Object Identifier)

10.3934/dcds.2019004
Discrete and continuous dynamical systems. Series A, Vol. 39, Issue 1 (January 2019) , p. 75-113

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