Complex integrability and linearizability of cubic Z2-equivariant systems with two 1:q resonant singular points

被引：18

作者：

Li, Feng ^{[1
]}

Liu, Yuanyuan ^{[1
]}

Yu, Pei ^{[2
]}

Wang, Jinliang ^{[3
]}

机构：

[1] Linyi Univ, Sch Math & Stat, Linyi 276005, Shandong, Peoples R China

[2] Western Univ, Dept Appl Math, London, ON N6A 5B7, Canada

[3] Heilongjiang Univ, Sch Math Sci, Harbin 150080, Heilongjiang, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2021年 / 300卷

基金：

中国国家自然科学基金; 加拿大自然科学与工程研究理事会;

关键词：

Integrability; Linearizability; Saddle value; Periodic constant; Resonant node; BI-CENTER PROBLEM; 12; LIMIT-CYCLES;

D O I：

10.1016/j.jde.2021.08.015

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, complex integrability and linearizability of cubic Z(2)-equivariant systems with two 1 :q resonant singular points are investigated, and the necessary and sufficient conditions on complex integrability and linearizability of the systems with two 1: (- q) resonant saddles are obtained for q = 1, 2, 3, 4. Moreover, for general positive integer q, the complex integrability and linearizability conditions are classified, and the sufficiency of the conditions is proved. Further, the linearizability conditions of cubic Z(2)-equivariant systems with two 1:q resonant node points are also classified. (C) 2021 Elsevier Inc. All rights reserved.

引用

页码：786 / 813

页数：28