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 Email
Junliang Lu Email
Xiaochun Hong Email