Bulletin des Sciences MathématiquesVolume 157, December 2019, 102796Cubic perturbations of symmetric elliptic Hamiltonians of degree four in a complex domainAuthor links open overlay panelBassem Ben Hamed a, Ameni Gargouri b, Lubomir Gavrilov cShow moreShareCitehttps://doi.org/10.1016/j.bulsci.2019.102796Get rights and contentUnder an Elsevier user licenseopen archiveAbstractWe consider arbitrary one-parameter cubic deformations of the Duffing oscillator x″=x−x3. In the case when the first Melnikov function M1 vanishes, but M2≠0 we compute the general form of M2 and study its zeros in a suitable complex domain.Previous article in issueNext article in issueKeywordsLimit cyclesZeros of elliptic integralsDuffing oscillatorRecommended articlesCited by (0)© 2019 Elsevier Masson SAS.