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

报告人：孙宪波教授，杭州师范大学

报告时间：2024年5月18日（星期六）10:00-11:00

报告地点：20-200

报告摘要：We study the limit cycles that bifurcate from a heteroclinic loop in a cubic non-elliptic Hamiltonian system by Melnikov functions of any order. The heteroclinic loop connects a non-Morse point and a hyperbolic saddle. We establish the asymptotic expansions of the Melnikov functions near this heteroclinic loop in near-Hamiltonian systems and provide the formulas of its first seven coefficients. For the cubic degenerate Hamiltonian system we derive the expressions of all different order Melnikov functions.The asymptotic expansions of all nonzero Melnikov functions are exactly obtained. Using these expansions, we obtain 3, 5, 6 and 1 limit cycle bifurcating from the heteroclinic loop by the first, second, third and forth order Melnikov functions, respectively.

报告人简介：孙宪波，教授，博士生导师。研究方向为微分方程定性理论及其应用，在JDE，SCM，DCDS B，JSC，BSM等国际主流SCI期刊上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**青年基金在内的省部级项目。