一类五次多项式系统无穷远点的中心条件与赤道极限环分支

Center conditions and bifurcation at the equator for a class of quintic polynomial system

研究一类五次多项式系统无穷远点的中心条件与赤道极限环分支.用一同胚变换将无穷远点转变成原点(初等奇点).用计算机代数系统Mathematica计算了这个多项式系统无穷远点的前55个奇点量,并由此得到了无穷远点的中心条件.通过参数的微小扰动,首次给出了一个在无穷远点有9个极限环的五次多项式系统的实例.

Center conditions and bifurcation of limit cycles at the infinity for a class of quintic polynomial system were studied. The method was based on a homeomorphic transformation of the infinity into the origin （linear singular point）. The first 55 singular point quantities for the infinity were computed by computer algebra system Mathematica, and the center conditions for the infinity were derived at the same time. A quintic polynomial system, which bifurcates 9 limit cycles from the equator, was obtained at the first time by small perturbation of parameters.