三维微分系统中心流形上的等时中心  

The Isochronous Center on Center Manifolds for Three Dimensional Differential Systems

作　　者：黄文韬 王勤龙 杜超雄 Wen Tao HUANG;Qin Long WANG;Chao Xiong DU(Center for Applied Mathematics of Guangxi(GXNU),College of Mathematics and Statistics,Guangxi Normal University,Guilin 541006,P.R.China;Center for Applied Mathematics of Guangxi(GUET),School of Mathematics and Computational Science,Guilin University of Electronic Technology,Guilin 541004,P.R.China;School of Mathematics,Changsha Normal University,Changsha 410100,P.R.China)

机构地区：[1]广西应用数学中心(GXNU)广西师范大学数学与统计学院,桂林541006 [2]广西应用数学中心(GUET)桂林电子科技大学数学与计算科学学院,桂林541004 [3]长沙师范学院数学学院,长沙410100

出　　处：《数学学报（中文版）》2024年第5期995-1008,共14页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(12061016,12161023);广西科技计划项目(2020GXNSFAA159138);广西高校中青年教师科研基础能力提升项目(2022KY0254);广西应用数学中心基地项目(桂科AD21220114)。

摘　　要：本文给出了研究一类三维多项式微分系统中心流形上等时中心的直接方法.首先,定义了三维系统的等时常数,并给出了求等时常数的递推公式,由此,不经中心流形而直接计算等时常数确定等时性的必要条件.在应用部分,解决了两类具体系统的等时中心问题.该方法是平面微分系统刘一戎奇点量计算形式级数方法的推广与发展.其算法是线性的,十分便于计算机代数系统来实现.In this paper,we present a method to study isochronous centers in 3-dimensional polynomial differential systems.Firstly,the isochronous constants of the three dimensional system are defined and recursive formulas to obtain them are given.The conditions for the isochronicity of a center are determined by the computation of isochronous constants for which there is no need to compute center manifolds of the three dimensional systems.Then the isochronous center conditions of two specific systems are discussed as an application of our method.Our method is a generalization of the formal series method proposed by Yirong Liu for determining the order of a fine focus of planar differential systems.This method with the recursive formulas can be easily implemented on a computer using a computer algebra system.

关 键 词：三维系统 等时中心 中心流形 等时常数 

分 类 号：O19[理学—数学]