Upper Bound of the Number of Zeros for Abelian Integrals in a Kind of Quadratic Reversible Centers of Genus One
Year: 2024
Author: Qiuli Yu, Houmei He, Yuangen Z han, Xiaochun Hong
Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 1 : pp. 218–227
Abstract
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 $n.$
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2024.218
Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 1 : pp. 218–227
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: Abelian integral quadratic reversible center weakened Hilbert’s 16th problem Picard-Fuchs equation Riccati equation.