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

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

Year:    2020

Author:    Lijun Hong, Junliang Lu, Xiaochun Hong

Journal of Nonlinear Modeling and Analysis, Vol. 2 (2020), Iss. 2 : pp. 161–171

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 $n$.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

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

Journal of Nonlinear Modeling and Analysis, Vol. 2 (2020), Iss. 2 : pp. 161–171

Published online:    2020-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    11

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

Author Details

Lijun Hong

Junliang Lu

Xiaochun Hong