论文信息 - A cubic system with thirteen limit cycles

A cubic system with thirteen limit cycles

Abstract We construct a planar cubic system and demonstrate that it has at least 13 limit cycles. The construction is essentially based on counting the number of zeros of some Abelian integrals.

[1] Jibin Li,et al. Hilbert's 16th Problem and bifurcations of Planar Polynomial Vector Fields , 2003, Int. J. Bifurc. Chaos.

[2] Freddy Dumortier,et al. Perturbation from an elliptic Hamiltonian of degree four—III global centre , 2003 .

[3] Songling Shi,et al. A CONCRETE EXAMPLE OF THE EXISTENCE OF FOUR LIMIT CYCLES FOR PLANE QUADRATIC SYSTEMS , 1980 .

[4] Colin Christopher,et al. Limit Cycles of Differential Equations , 2007 .

[5] Li Xin Cheng,et al. On Hereditarily Indecomposable Banach Spaces , 2006 .

[6] Pei Yu,et al. Twelve Limit Cycles in a cubic Case of the 16TH Hilbert Problem , 2005, Int. J. Bifurc. Chaos.

[7] Noel G. Lloyd,et al. Polynomial systems: a lower bound for the Hilbert numbers , 1995, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[8] Chengzhi Li,et al. Perturbation from an elliptic Hamiltonian of degree four—IV figure eight-loop , 2003 .