We study pseudo-Abelian integrals associated with polynomial perturbations of Darboux integrable system with a triple point. Under some assumptions, we prove the local boundedness of the number of their zeros. Assuming that this is the only non-genericity, we prove that the number of zeros of the corresponding pseudo-Abelian integrals is bounded uniformly for nearby Darboux integrable foliations.

中文翻译：

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具有三点和伪阿贝尔积分的Darboux可积系统

我们研究与带三点的Darboux可积系统的多项式摄动有关的伪阿贝尔积分。在某些假设下，我们证明了其零个数的局部有界性。假设这是唯一的非泛型，我们证明了对应的伪阿贝尔积分的零点数目对于附近的Darboux可积叶面是有界的。