Bifurcations of Limit Cycles from a Quintic Hamiltonian System with a Heteroclinic Cycle
In this paper,we consider Li′enard systems of the form dx/dt=y,dy/dt=x＋bx3-x5＋ε（α＋βx2＋γx4）y,where b∈R,0〈｜ε｜〈〈1,（α,β,γ）∈D∈R3 and D is bounded.We prove that for ｜b｜〉〉1（b〈0） the least upper bound of the number of isolated zeros of the related Abelian integrals I（h）=∮Γh（α＋βx2＋γx4）ydx is 2（counting the m...
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| Veröffentlicht in: | Acta mathematica Sinica. English series 2014-03, Vol.30 (3), p.411-422 |
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| creator | Zhao, Li Qin Li, De Ping |
| description | In this paper,we consider Li′enard systems of the form dx/dt=y,dy/dt=x＋bx3-x5＋ε（α＋βx2＋γx4）y,where b∈R,0〈｜ε｜〈〈1,（α,β,γ）∈D∈R3 and D is bounded.We prove that for ｜b｜〉〉1（b〈0） the least upper bound of the number of isolated zeros of the related Abelian integrals I（h）=∮Γh（α＋βx2＋γx4）ydx is 2（counting the multiplicity） and this upper bound is a sharp one. |
| doi_str_mv | 10.1007/s10114-014-2615-8 |
| format | Article |
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| subjects | Abel积分 Mathematics Mathematics and Statistics Polynomials 哈密顿系统 多样性 异宿环 最小上界 有界 极限环 |
| title | Bifurcations of Limit Cycles from a Quintic Hamiltonian System with a Heteroclinic Cycle |
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