摘要
讨论一类具有4个双曲鞍点和5个中心奇点的三次哈密顿系统,存在一个由4个鞍点和连接它们的异宿轨道组成的奇异环S(4)及4个分别由2个鞍点和连接它们的异宿轨道组成的奇异环S(2).利用定性分析和分支理论等方法,对这类三次哈密顿系统在五次多项式扰动下的奇异环分支问题进行了研究,得出在适当的扰动下系统至少可产生14个极限环,并给出了它们的分布.
A kind of cubic Hamilton system with four hyperbolic saddle points and five central singular points is discussed. This system consists of a singular cycle S^4~ with four saddle points and heteroclinic orbits connecting them, and four singular cycles S12） with two saddle points and heteroelinie orbits connecting them respectively. By using the method of the qualitative analysis and bifurcation theory, the singular cycle bifurcation of such cubic Hamilton system under five-order perturbation is analyzed. At least fourteen limit cycles exist under suitable perturbation and their distribu- tions are given.
出处
《天津师范大学学报（自然科学版）》
CAS
2013年第2期1-9,共9页
Journal of Tianjin Normal University：Natural Science Edition
基金
国家自然科学基金资助项目(11271046)
