On the Number of Zeros of Abelian Integrals for a Class of Quadratic Reversible Centers of Genus One

Authors

  • Lijun Hong
  • Junliang Lu School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming,Yunnan 650221, China 
  • Xiaochun Hong

DOI:

https://doi.org/10.12150/jnma.2020.161

Keywords:

Abelian integral, Quadratic reversible center, Weakened Hilbert's 16th problem, Limit cycle.

Abstract

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 $n$.

Downloads

Published

2024-04-10

Abstract View

  • 22562

Pdf View

  • 2483

Issue

Vol. 2 No. 2 (2020)

Section

Articles

How to Cite

On the Number of Zeros of Abelian Integrals for a Class of Quadratic Reversible Centers of Genus One. (2024). Journal of Nonlinear Modeling and Analysis, 2(2), 161-171. https://doi.org/10.12150/jnma.2020.161