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On the Number of Zeros of Abelian Integrals for aClass of Quadratic Reversible Centers of GenusOne
  
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KeyWord:Abelian integral  Quadratic reversible center  Weakened Hilbert's 16th problem  Limit cycle
Author NameAffiliation
Lijun Hong School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China 
Junliang Lu School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China 
Xiaochun Hong School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China 
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Abstract:
      In this paper, using the method of Picard-Fuchs equation and Ric- cati equation, for a class of quadratic reversible centers of genus one, we re- search 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.