A Linear Estimation To The Number Of Zeros For Abelian Integrals In A Kind Of Quadratic Reversible Centers Of Genus One

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION（2020）

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摘要

In this paper, using the method of Picard-Fuchs equation and Riccati equation, we consider the number of zeros for Abelian integrals in a kind of quadratic reversible centers of genus one under arbitrary polynomial perturbations of degree n, and obtain that the upper bound of the number is 2 [(n + 1)/2]+ [n/2] + 2 (n >= 1), which linearly depends on n.

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关键词

Abelian integral,quadratic reversible center,weakened Hilbert's 16th problem,limit cycle.

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