Bounding the number of zeros of certain Abelian integrals

被引：79

作者：

Manosas, F. ^{[2
]}

Villadelprat, J. ^{[1
]}

机构：

[1] Univ Barcelona, Dept Matemat Aplicada & Anal, Barcelona, Spain

[2] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Spain

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2011年 / 251卷 / 06期

关键词：

Abelian integral; Chebyshev system; Wronskian; Hamiltonian perturbation; Limit cycle; LIMIT-CYCLES; PERTURBATIONS; SYSTEMS; CENTERS;

D O I：

10.1016/j.jde.2011.05.026

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we prove a criterion that provides an easy sufficient condition in order for any nontrivial linear combination of n Abelian integrals to have at most n + k - 1 zeros counted with multiplicities. This condition involves the functions in the integrand of the Abelian integrals and it can be checked, in many cases, in a purely algebraic way. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：1656 / 1669

页数：14

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