J. Nonl. Mod. Anal., 6 (2024), pp. 218-227.
Published online: 2024-03
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By using the methods of Picard-Fuchs equation and Riccati equation, we study the upper bound of the number of zeros for Abelian integrals in a kind of quadratic reversible centers of genus one under polynomial perturbations of degree $n.$ We obtain that the upper bound is $7[(n − 3)/2] + 5$ when $n ≥ 5, 8$ when $n = 4, 5$ when $n = 3, 4$ when $n = 2,$ and $0$ when $n = 1$ or $n = 0,$ which linearly depends on $n.$
}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2024.218}, url = {http://global-sci.org/intro/article_detail/jnma/22977.html} }By using the methods of Picard-Fuchs equation and Riccati equation, we study the upper bound of the number of zeros for Abelian integrals in a kind of quadratic reversible centers of genus one under polynomial perturbations of degree $n.$ We obtain that the upper bound is $7[(n − 3)/2] + 5$ when $n ≥ 5, 8$ when $n = 4, 5$ when $n = 3, 4$ when $n = 2,$ and $0$ when $n = 1$ or $n = 0,$ which linearly depends on $n.$