On the saddle order of polynomial differential systems at a resonant singular point

被引：2

作者：

Doug, Guangfeng ^{[1
]}

Yang, Jiazhong ^{[2
]}

机构：

[1] Sun Yat Sen Univ, Dept Math, Guangzhou 510275, Guangdong, Peoples R China

[2] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2015年 / 423卷 / 02期

关键词：

Focus order; Saddle order; Polynomial differential systems; Integrability; p : -q Resonance; VECTOR-FIELDS; CENTERS;

D O I：

10.1016/j.jmaa.2014.10.085

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the complexity of integrability of planar polynomial differential systems whose eigenvalues admit resonances at a saddle singular point. We prove that for arbitrary integer n >= 2, if one of n + 2 and 2n + 1 is a prime number, then there exists a polynomial differential system of degree n with 1 : -2 resonance at its saddle singular point such that the saddle order can be as high as n(2) - 1. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：1557 / 1569

页数：13