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.