JournalsaihpcVol. 32, No. 2pp. 307–324

Perturbations of quadratic Hamiltonian two-saddle cycles

  • Lubomir Gavrilov

    Institut de Mathématiques de Toulouse, UMR 5219, Université de Toulouse, CNRS, UPS IMT,F-31062 Toulouse Cedex 9, France

  • Iliya D. Iliev

    Institute of Mathematics, Bulgarian Academy of Sciences, Bl. 8, 1113 Sofia, Bulgaria
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Abstract

We prove that the number of limit cycles which bifurcate from a two-saddle loop of a planar quadratic Hamiltonian system, under an arbitrary quadratic deformation, is less than or equal to three.

Cite this article

Lubomir Gavrilov, Iliya D. Iliev, Perturbations of quadratic Hamiltonian two-saddle cycles. Ann. Inst. H. Poincaré Anal. Non Linéaire 32 (2015), no. 2, pp. 307–324

DOI 10.1016/J.ANIHPC.2013.12.001