一类四次哈密尔顿系统的极限环数

摘要

研究在高次扰动项下的四次哈密尔顿系统,通过数值方法计算Abel积分的零点个数,得到该系统存在至少14个极限环的结论,这是四次哈密尔顿系统在四次扰动下关于极限环个数的较好结果.%The quartic Hamilton system with quartic perturbed terms is studied. By using the accurate method to calculate the number of zeros of Abel integrals of the system, it is obtained that the system has at least 14 limit cycles.