The number and distributions of limit cycles for a class of cubic near-Hamiltonian systems
The paper concerns the number and distributions of limit cycles for a cubic Hamiltonian system under cubic perturbation which has 5 centers and 4 saddles. By using the idea of changing the stability of a homoclinic loop, it is proved that such system can have 9-11 limit cycles. The main result consists in finding two new distributions of 11 limit cycles for a cubic system. Such previous distributions are presented in the following works: 1. \textit{M. Han, Y. Wu} and \textit{P. Bi} [Discrete Contin. Dyn. Syst. 12, No. 4, 675--686 (2005; Zbl 1085.34027)]. 2. \textit{M. Han, T. Zhang} and \textit{H. Zang} [Int. J. Bifurcation Chaos Appl. Sci. Eng. 14, No. 12, 4285--4292 (2004; Zbl 1090.34025)].
scientific article; zbMATH DE number 5016210