Bifurcation of Limit cycles from a heteroclinic loop connecting a tangent non-Morse point and a hyperbolic saddle by Melnikov functions of any order

主 讲 人 ：孙宪波    教授

活动时间：08月02日11时00分    

地      点 ：理科群1号楼D311室

讲座内容：

We study the limit cycles that bifurcate from a heteroclinic loop in a cubic non-elliptic Hamiltonian system by Melnikovfunctions of any order. The heteroclinic loop connects a non-Morse point and a hyperbolic saddle. We establishthe asymptotic expansions of the Melnikov functions near thisheteroclinic loop in near-Hamiltonian systems and provide the formulas of its first seven coefficients. For the cubicdegenerate Hamiltonian system we derive the expressions ofall different order Melnikov functions.The asymptotic expansions of all nonzeroMelnikov functions are exactly obtained. Using these expansions, we obtain 3, 5, 6 and 1 limit cycles bifurcating fromthe heteroclinic loop by the first, second, third and forth orderMelnikov functions, respectively.

主讲人介绍：

孙宪波，杭州师范大学数学学院教授，博士生导师。研究方向为微分方程定性理论，在中国科学，DCDS B，JDE，JSC，BSM等知名期刊发表学术论文三十余篇，主持两项国家自然科学基金，多项含广西杰出青年基金在内的省部级项目。

发布时间：2024-07-31 19:21:07