Painlevé Property and Integrability of Polynomial Dynamical Systems  

作　　者：Li Wen-lei Shi Shao-yun 

机构地区：[1]School of Mathematics, Jilin University [2]Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University

出　　处：《Communications in Mathematical Research》2014年第4期358-368,共11页数学研究通讯（英文版）

基　　金：The NSF (11371166,11301210)of China;National 973 Project (2012CB821200) of China;Jilin Province Youth Science Foundation

摘　　要：The main purpose of this paper is to investigate the connection between the Painlev′e property and the integrability of polynomial dynamical systems. We show that if a polynomial dynamical system has Painlev′e property, then it admits certain class of first integrals. We also present some relationships between the Painlev′e property and the structure of the differential Galois group of the corresponding variational equations along some complex integral curve.The main purpose of this paper is to investigate the connection between the Painlev′e property and the integrability of polynomial dynamical systems. We show that if a polynomial dynamical system has Painlev′e property, then it admits certain class of first integrals. We also present some relationships between the Painlev′e property and the structure of the differential Galois group of the corresponding variational equations along some complex integral curve.

关 键 词：Painlev′e property INTEGRABILITY differential Galois group 

分 类 号：O19[理学—数学]