作 者: ;
机构地区: 深圳大学理学院
出 处: 《数学杂志》 2004年第5期565-569,共5页
摘 要: 对Bogdanov Takens向量场的三次齐次扰动系统进行了讨论 ,得到了当其前二阶Melnikov函数恒为 0时 ,则其后各阶Melnikov函数一定为 0 ,且对于小的扰动参数 ,此系统为可积的或为Hamilton的 ;并对M1 (h)≠0和M1 (h)≡ 0 ,M2 (h)≠ In this paper, we discuss the bifurcation problem of cubic homogeneous perturbation with Bogdanov-Takens vector fields. We prove that if M_1(h)=M_2(h)≡0,then M_k(h)≡0(k≥3) and the system is Hamiltonian or integrable for sufficiently small perturbation parameter, On the other hand, we analyse the bifurcation structure when M_1(h)≠0 and M_1(h)≡0,M_2(h)≠0.