Upper Bound of the Number of Zeros for Abelian Integrals in a Kind of Quadratic Reversible Centers of Genus One |
| |
Authors: | Qiuli Yu Houmei He Yuangen Zhan Xiaochun Hong |
| |
Affiliation: | School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China;Department of Information Engineering, Jingdezhen Ceramic University, Jingdezhen, Jiangxi 333403, China |
| |
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 $nge 5$, $8$ when $n=4$, $5$ when $n=3$, $4$ when $n=2$, and $0$ when $n=1$ or $n=0$, which linearly depends on $n$. |
| |
Keywords: | Abelian integral quadratic reversible center weakened Hilbert''s 16th problem Picard-Fuchs equation Riccati equation |
|
| 点击此处可从《Journal of Nonlinear Modeling and Analysis》浏览原始摘要信息 |
|
点击此处可从《Journal of Nonlinear Modeling and Analysis》下载免费的PDF全文 |
|