Local integrability of a family of three-dimensional quadratic systems

被引：12

作者：

Hu, Zhaoping ^{[1
,3
]}

Han, Maoan ^{[2
]}

Romanovski, Valery G. ^{[3
,4
]}

机构：

[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

[2] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

[3] Univ Maribor, Ctr Appl Math & Theoret Phys, SI-2000 Maribor, Slovenia

[4] Univ Maribor, Fac Nat Sci & Math, SI-2000 Maribor, Slovenia

来源：

PHYSICA D-NONLINEAR PHENOMENA | 2013年 / 265卷

关键词：

Analytic first integrals; Integrability variety; Reversibility; Invariant plane; Darboux integrability; LOTKA-VOLTERRA SYSTEMS; ANALYTIC NORMALIZATION; EMBEDDING FLOWS; LINEARIZABILITY; INTEGRALS;

D O I：

10.1016/j.physd.2013.09.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the local integrability of a family of three dimensional quadratic systems in a neighborhood of (0 : -1 : 1) resonant singular point. We find the necessary and sufficient conditions for the existence of two functionally independent first integrals of the system. Mechanisms for integrability for the systems are either time-reversibility or Darboux integrability. (C) 2013 Elsevier B.V. All rights reserved.

引用

页码：78 / 86

页数：9

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