Reversibility and quasi-homogeneous normal forms of vector fields

被引：19

作者：

Algaba, A. ^{[2
]}

Garcia, C. ^{[2
]}

Teixeira, M. A. ^{[1
]}

机构：

[1] Univ Estadual Campinas, IMECC, Dept Math, Campinas, SP, Brazil

[2] Univ Huelva, Fac Ciencias, Dept Math, Huelva, Spain

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2010年 / 73卷 / 02期

关键词：

Reversibility; Quasi-homogeneous system; Normal form; Singularity; Center; NILPOTENT CENTERS; INTEGRABILITY; SYSTEMS;

D O I：

10.1016/j.na.2010.03.046

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper uses tools in quasi-homogeneous normal form theory to discuss certain aspects of reversible vector fields around an equilibrium point. Our main result provides an algorithm, via Lie Triangle, that detects the non-reversibility of vector fields. That is, it is possible to decide whether a planar center is not reversible. Some of the theory developed is also applied to get further results on nilpotent and degenerate polynomial vector fields. We find several families of nilpotent centers which are non-reversible. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：510 / 525

页数：16

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