坐标变换下平面解析系统单值轨道的不变性  

Invariance of monodromic orbits of planar analytic system under coordinate transformation

作　　者：郭春 黄土森[1] GUO Chun;HUANG Tusen(School of Science,Zhejiang Sci-Tech University,Hangzhou 310018,China)

机构地区：[1]浙江理工大学理学院,杭州310018

出　　处：《浙江理工大学学报（自然科学版）》2023年第6期775-783,共9页Journal of Zhejiang Sci-Tech University(Natural Sciences)

基　　金：国家自然科学基金项目(11671359,11672270)。

摘　　要：为了研究平面解析系统在何种坐标变换下单值轨道具有不变性,首先给出平面解析系统的轨线沿固定方向进入奇点的两个定义,并证明了它们是等价的;其次引入判别轨线沿固定方向进入奇点的一个充要条件,得到平面解析系统在非正则变换下系统轨道可以具有不同的单值性;最后通过对平面解析系统做正则变换,证明了变换前后的系统轨线具有相同的单值性。该结果对研究平面解析系统单值轨道的不变性具有参考价值。In order to study the invariance of monodromic orbits under which coordinate transformation of planar analytic system,firstly,two definitions of orbits of planar analytic system entering singular point along a fixed direction are given,and they are proved to be equivalent.Secondly,a necessary and sufficient condition for discriminating that orbits enter singular point along a fixed direction is introduced,and it is obtained that the orbits for the planar analytic system and the associated system under non-regular coordinate transformation have a different monodromy.Finally,by making a regular coordinate transformation on the planar analytic system,it is proved that the orbits for the planar analytic system and the associated system have the same monodromy.The result can provide a reference for studying the invariance of monodomic orbits of planar analytic system.

关 键 词：平面解析系统 轨线 奇点 单值性问题 正则坐标变换 

分 类 号：O175.14[理学—数学]