Estimating the Number of Zeros for Abelian Integrals of Quadratic Reversible Centers with Orbits Formed by Higher-Order Curves

被引：10

作者：

Hong, Xiaochun ^{[1
]}

Xie, Shaolong ^{[2
]}

Chen, Longwei ^{[3
]}

机构：

[1] Yunnan Univ Finance & Econ, Sch Math & Stat, Yunnan TongChuang Sci Comp & Data Min Res Ctr, Kunming 650221, Yunnan, Peoples R China

[2] Yuxi Normal Univ, Sch Business, Yuxi 653100, Yunnan, Peoples R China

[3] Yunnan Univ Finance & Econ, Sch Math & Stat, Kunming 650221, Yunnan, Peoples R China

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2016年 / 26卷 / 02期

关键词：

Quadratic reversible center; Abelian integral; weakened 16th Hilbert problem; LIMIT-CYCLES; GLOBAL BIFURCATION; LINEAR ESTIMATE; ALMOST-ALL; CYCLICITY; SYSTEM; FAMILY;

D O I：

10.1142/S0218127416500206

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this study, we determine the associated number of zeros for Abelian integrals in four classes of quadratic reversible centers of genus one. Based on the results of [Li et al., 2002b], we prove that the upper bounds of the associated number of zeros for Abelian integrals with orbits formed by conics, cubics, quartics, and sextics, under polynomial perturbations of arbitrary degree n, depend linearly on n.

引用

页数：16

共 26 条

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[24] Existence of Solutions with a Given Number of Zeros to a Higher-Order Regular Nonlinear Emden-Fowler Equation
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[25] ESTIMATING THE SMOOTHNESS OF A GAUSSIAN RANDOM FIELD FROM IRREGULARLY SPACED DATA VIA HIGHER-ORDER QUADRATIC VARIATIONS
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[26] ON THE EXISTENCE OF SOLUTIONS TO HIGHER-ORDER REGULAR NONLINEAR EMDEN-FOWLER TYPE EQUATIONS WITH GIVEN NUMBER OF ZEROS ON THE PRESCRIBED INTERVAL
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