关于周期函数的研究  

Study of Period Functions

作　　者：李承治[1] Li Chengzhi(School of Mathematical Sciences,Peking University,Beijing 100871,China)

机构地区：[1]北京大学数学科学学院,北京100871

出　　处：《数学理论与应用》2023年第1期1-31,共31页Mathematical Theory and Applications

摘　　要：在这篇综述中我们首先简要介绍平面光滑(或解析)向量场的周期函数的概念,以及它的等时性、单调性和临界周期的个数.然后我们介绍本领域中一些重要的结果,特别是关于等时中心,关于椭圆函数或超椭圆函数所导出的向量场的周期函数,和关于二次可积系统的周期函数.除了这些结果,我们在第六节中还列出一些相关的猜想和问题,这可以作为进一步研究的论题.In this survey article we first briefly introduce some concepts related to the period function of a planar smooth(or analytic)vector field,and its isochronicity,monotonicity,and the number of critical periods.Then,we introduce some important results in this field,especially about the isochronous centers,the period functions associated to the elliptic and hyperelliptic Hamiltonian functions,and the period functions of quadratic integrable systems.Besides these results we list some conjectures and problems in Section 6,which may provide topics for further studies.

关 键 词：周期函数 等时性 单调性 临界周期 

分 类 号：O174[理学—数学]