News & Announcements
Links
Upper Bound of the Number of Zeros for Abelian Integrals in a Kind of Quadratic Reversible Centers of Genus One
  
View Full Text  View/Add Comment  Download reader
KeyWord:Abelian integral, quadratic reversible center, weakened Hilbert's 16th problem, Picard-Fuchs equation, Riccati equation
Author NameAffiliation
Qiuli Yu School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China 
Houmei He School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China 
Yuangen Zhan Department of Information Engineering, Jingdezhen Ceramic University, Jingdezhen, Jiangxi 333403, China 
Xiaochun Hong School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China 
Hits: 56
Download times: 52
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 $n\ge 5$, $8$ when $n=4$, $5$ when $n=3$, $4$ when $n=2$, and $0$ when $n=1$ or $n=0$, which linearly depends on $n$.