Geodesic
Limit Cycles of Perturbations of a Class of Quadratic Hamiltonian Vector Fields
Serdica Mathematical Journal, Tome 22 (1996) no. 2, pp. 91-108

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We prove that in quadratic perturbations of generic Hamiltonian vector fields with two saddle points and one center there can appear at most two limit cycles. This bound is exact.
Keywords: Limit Cycles, Abelian Integrals, Picard-Lefschetz Formula 
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     title = {Limit {Cycles} of {Perturbations} of a {Class} of {Quadratic} {Hamiltonian} {Vector} {Fields}},
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Markov, Yavor. Limit Cycles of Perturbations of a Class of Quadratic Hamiltonian Vector Fields. Serdica Mathematical Journal, Tome 22 (1996) no. 2, pp. 91-108. http://geodesic.mathdoc.fr/item/SMJ2_1996_22_2_a2/