一类双中心可积系统在齐三次扰动下的Poincare分支问题研究

Poincare Bifurcation of Integrable System with Double Center Perturbed by Cubic Homogeneous Polynomial

研究了一类双中心可积系统在齐三次扰动下的Poincare分支问题。先将Abel积分表示为几个基本积分的线性组合的形式，然后将其零点的问题转化为多项式零点的问题，其中没有出现第一与第二型完全椭圆积分，减小了求解难度，最后证明得出该系统分支出极限环数目的最小上界为1。

The Poincare bifurcation of integrable system with double center perturbed by cubic homogeneous polynomial was studied.First the Abelian integrals were expressed into the linear combination of several basic integrals,thus the problem of number of zero was turned into one of the polynomial zeros,where the elliptic integral of the first or second kind was not appeared.Finally the least upper bound of number on limit cycle 1 is obtained and proved.