不定奇异径向对称系统周期轨的存在性  

Existence of Periodic Orbits for a Radial Symmetric System with an Inde nite Singularity

作　　者：张秀强 梁载涛 何瑞瑞 ZHANG Xiuqiang;LIANG Zaitao;HE Ruirui(School of Mathematics and Big Data,Anhui University of Science and Technology,Huainan 232001,China)

机构地区：[1]安徽理工大学数学与大数据学院,安徽淮南232001

出　　处：《应用数学》2024年第3期579-588,共10页Mathematica Applicata

基　　金：安徽省自然科学基金(2308085MA06);安徽高校自然科学研究项目(2022AH040112)。

摘　　要：本文主要研究具有不定奇异点的径向对称系统周期轨的存在性.运用拓扑度理论,证明了该系统存在两族不同的周期轨:一族以小角动量绕原点旋转,另一族以大角动量和大振幅绕原点旋转.本文的结果既适用于强奇性的情况,也适用于弱奇性的情况.In this paper,the existence of periodic orbits for a radial symmetric system with an indefinite singularity is studied.Based on the topological degree theory,we show the existence of two distinct families of periodic orbits:one rotates around the origin with small angular momentum,and the other one rotates around the origin with both large angular momentum and large amplitude.Our results are applicable to both the case of a strong singularity and the case of a weak singularity.

关 键 词：周期轨 径向对称系统 不定奇异点 拓扑度理论 

分 类 号：O175.12[理学—数学]