Abelian integral

in this paper, a method of finding stable approximate solution of nonlinear abelian integral equation is given by using regularization method.

本文利用正则化方法给出了非线性阿贝耳积分方程稳定近似解的求法。

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for the former, it is proved that the system under the polynomial perturbations has at most [ n/ 2] limit cycles in the finite plane and the upper bound is sharp. the proof relies on a careful analysis of a related abelian integral.

第四章考虑了两类可积非哈密顿系统，对于其中的一类得到了有限平面内在n次多项式扰动下分支出的极限环的个数的上确界是[n/2]。

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for the latter, we obtain the linear estimation of the number of isolated zeros of the corresponding abelian integral.

对于另一类得到了其相应的阿贝尔积分的孤立零点的估计。

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consider the abelian integral for a non-hamilton system with quadratic perturbation and get that the lowest upper bound of the number of zeros of the abelian integral is 2. also, some sufficient conditions for the unique zero of the abelian integral are obtained.

对一类可积非Hamilton系统的二次扰动系统的Abelian积分进行了讨论，得到了其零点数的最小上界为2，并给出了Abelian积分存在唯一零点的一些充分条件。

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