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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 21n24(n3), 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 Email

Junliang Lu Email

Xiaochun Hong Email