TY - JOUR
T1 - Upper Bound of the Number of Zeros for Abelian Integrals in a Kind of Quadratic Reversible Centers of Genus One
AU - Yu , Qiuli
AU - He , Houmei
AU - han , Yuangen Z
AU - Hong , Xiaochun
JO - Journal of Nonlinear Modeling and Analysis
VL - 1
SP - 218
EP - 227
PY - 2024
DA - 2024/03
SN - 6
DO - http://doi.org/10.12150/jnma.2024.218
UR - https://global-sci.org/intro/article_detail/jnma/22977.html
KW - Abelian integral, quadratic reversible center, weakened Hilbert’s
16th problem, Picard-Fuchs equation, Riccati equation.
AB - <p style="text-align: justify;">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 $n.$</p>