TY - JOUR
T1 - On the Number of Zeros of Abelian Integrals for a Class of Quadratic Reversible Centers of Genus One
AU - Hong , Lijun
AU - Lu , Junliang
AU - Hong , Xiaochun
JO - Journal of Nonlinear Modeling and Analysis
VL - 2
SP - 161
EP - 171
PY - 2021
DA - 2021/04
SN - 2
DO - http://doi.org/10.12150/jnma.2020.161
UR - https://global-sci.org/intro/article_detail/jnma/18804.html
KW - Abelian integral, Quadratic reversible center, Weakened Hilbert's
16th problem, Limit cycle.
AB - <p style="text-align: justify;">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 $n$.</p>