【作者】 李方方；

【导师】 胡彦霞；

【作者基本信息】 华北电力大学（北京） ， 应用数学， 2010， 硕士

【摘要】 本文基于李(Lie)群理论研究了二阶、三阶和n阶自治系统的可积性。主要内容和结果包括以下几个方面：(1)首先给出了二阶恰当自治系统所接受的单参数李群的生成元的一般形式,然后讨论了该系统的一些性质；给出了两类特殊形式的二阶自治系统所接受的单参数李群的生成元的一般形式,并由此构造了系统的一个积分因子。(2)基于李群理论,给出并证明了利用三阶自治系统所接受的两个单参数李群的生成元求该系统的积分因子的方法与结论。(3)对于n阶自治系统,当系统为保守系统时,讨论了其积分因子和首次积分的关系；当系统为非保守系统时,给出并证明了系统积分因子存在的充要条件。更多还原

【Abstract】 Based on Lie group theory, the integrability of second order, third order and n-th order autonomous system is studied. The main contents and results of this dissertation are included as following aspects:(1) The general form of generators of one-parameter Lie groups accepted by second order exact automatic system is given. Then, some properties of the system are discussed. At the same time, the general form of generators of one-parameter Lie group which is accepted by two particular classes of second order automatic systems is given, thus the integrating factor of the system is constructed.(2) Base on Lie group theory, the method to obtain the integrating factors of the third order autonomous system by using of two one-parameter Lie groups accepted by the system is given and shown.(3) For the n-th order system, the relation between integrating factors and first integrals of the system is discussed when it is conservative system; At the same time, the sufficient and necessary condition for the existence of integrating factors of the system is given and proved when it is non-conservative system.更多还原