Realization problems for limit cycles of planar polynomial vector fields

被引：0

作者：

Margalef-Bentabol, Juan ^{[1
,2
]}

Peralta-Salas, Daniel ^{[3
]}

机构：

[1] CSIC, Inst Estruct Mat, Madrid 28006, Spain

[2] Univ Carlos III Madrid, Grp Modelizac & Simulac Numer, Inst Gregorio Millan, Leganes 28911, Spain

[3] CSIC, Inst Ciencias Matemat, Madrid 28049, Spain

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2016年 / 260卷 / 04期

基金：

欧洲研究理事会;

关键词：

Limit cycle; Polynomial vector field; Integrating factor; Realization problem; CONFIGURATIONS; EXISTENCE; SYSTEMS;

D O I：

10.1016/j.jde.2015.10.044

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that for any finite configuration of closed curves Gamma subset of R-2, one can construct an explicit planar polynomial vector field that realizes Gamma, up to homeomorphism, as the set of its limit cycles with prescribed periods, multiplicities and stabilities. The only obstruction given on this data is the obvious compatibility relation between the stabilities and the parity of the multiplicities. The constructed vector fields are Darboux integrable and admit a polynomial inverse integrating factor. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：3844 / 3859

页数：16

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[2]

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[3]

Chavarriga J., 1997, PUBL MAT, V41, P41

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