Yang, Jihua; Zhang, Erli; Liu, Mei The cyclicity of period annuli of a class of quartic Hamiltonian systems. (Chinese. English summary) Zbl 1389.37038 Adv. Math., Beijing 46, No. 2, 243-251 (2017). Summary: In this paper, we prove that the cyclicity of period annuli for system \[ \mathop x\limits^ \cdot = 2y\left({b + c{x^2} + 2{y^2}} \right), \mathop y\limits^ \cdot = - 2x\left({a + 2{x^2} + c{y^2}} \right) \] under perturbations of polynomials with degree \(n\) is not more than \(3\left[ {\frac{{n - 1}}{4}} \right] + 12\left[ {\frac{{n - 3}}{4}} \right] + 22\) (taking into account the multiplicity), where \(a< 0, b< 0\) and \(c< - 2\). MSC: 37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010) 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations 34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations 34D10 Perturbations of ordinary differential equations Keywords:Hamiltonian system; abelian integral; Hilbert’s 16th problem; Picard-Fuchs equation PDFBibTeX XMLCite \textit{J. Yang} et al., Adv. Math., Beijing 46, No. 2, 243--251 (2017; Zbl 1389.37038)