逆积分因子研究综述
A survey on the inverse integrating factor
摘要：
平面微分系统的极限环与逆积分因子之间的关系最早见于Giacomini，Llibre和Viano于1996年发表的一篇文章中。从那时起，许多研究文章都致力于研究逆积分因子的性质及其与极限环及其分支的关系。本文是关于这一课题的所有结果的总结。我们包括一个列表的参考文献以及相应的相关结果，旨在尽可能详尽。尽管如此，该文件是独立的，在这样一种方式，所有的主要成果的逆积分因子的陈述和一个完整的概述的主题。每一节包含一个不同的问题，其中逆积分因子发挥作用：可积性问题，关系与李对称性，中心问题，消失集的逆积分因子，分支的极限环从任何一个周期环或从一个单值$ω$ -极限集和一些推广。
英文摘要：
The relation between limit cycles of planar differential systems and the inverse integrating factor was first shown in an article of Giacomini, Llibre and Viano appeared in 1996. From that moment on, many research articles are devoted to the study of the properties of the inverse integrating factor and its relation with limit cycles and their bifurcations. This paper is a summary of all the results about this topic. We include a list of references together with the corresponding related results aiming at being as much exhaustive as possible. The paper is, nonetheless, self-contained in such a way that all the main results on the inverse integrating factor are stated and a complete overview of the subject is given. Each section contains a different issue to which the inverse integrating factor plays a role: the integrability problem, relation with Lie symmetries, the center problem, vanishing set of an inverse integrating factor, bifurcation of limit cycles from either a period annulus or from a monodromic $ω$-limit set and some generalizations.
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