报告时间：10月13日下午16：00-17：00

报告地点：雁山图书馆第二会议室205

报告题目：Limitcycle bifurcations near double homoclinic and heteroclinic loops of a class ofcubic Hamiltonian systems

报告摘要：Inthis talk we introduce our recent results on the double homoclinic andheteroclinic bifurcations by perturbing a cubic Hamiltonian system withpolynomial perturbations of degree n. It is proved that 4[(n-3)/2]+[(n-2)/2]+2and  2[(n-1)/2] limit cycles can bebifurcated from the period annuli near the double homoclicic loop  and the heteroclinic loop, respectively. Thisresult improves the biggest lower bound on the number of the bifurcated limitcycles comparing with the known results for the related problems. To achieveour results we develop the techniques on calculating the base and the relativerelations of the elements in the base, formed partly by curve integralfunctions along ovals of level sets of the Hamiltonian function, which appearin the expansions of the first order Melnikov functions.

报告人简介：张祥，上海交通大学特聘教授，享受国务院特殊津贴。2018年入选欧洲科学与艺术院院士。主要从事常微分方程的定性、分支和可积理论，以及奇异摄动理论及其应用等方面的研究。代表性研究成果发表在《American J. Mathematics》、《Transaction of AmericanMathematical Society》、《Communications inMathematical Physics》、《J. Functional Analysis》、《J. Differential Equations》、等国际重要数学期刊上。