J. Nonl. Mod. Anal., 2 (2020), pp. 161-171.
Published online: 2021-04
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In this paper, using the method of Picard-Fuchs equation and Riccati equation, for a class of quadratic reversible centers of genus one, we research the upper bound of the number of zeros of Abelian integrals for the system $(r10)$ under arbitrary polynomial perturbations of degree $n$. Our main result is that the upper bound is $21n − 24 (n ≥ 3)$, and the upper bound depends linearly on $n$.
}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2020.161}, url = {http://global-sci.org/intro/article_detail/jnma/18804.html} }In this paper, using the method of Picard-Fuchs equation and Riccati equation, for a class of quadratic reversible centers of genus one, we research the upper bound of the number of zeros of Abelian integrals for the system $(r10)$ under arbitrary polynomial perturbations of degree $n$. Our main result is that the upper bound is $21n − 24 (n ≥ 3)$, and the upper bound depends linearly on $n$.