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Limit cycles of a perturbation of a polynomial Hamiltonian systems of degree 4 symmetric with respect to the origin. (English) Zbl 1451.34033

Summary: 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.

MSC:

34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations
34C08 Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.)
34E10 Perturbations, asymptotics of solutions to ordinary differential equations
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