Local first integrals of differential systems and diffeomorphisms
Local first integrals of differential systems and diffeomorphisms
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DOI：
10.1007/s000330300003
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发表时间：
2003-03
期刊：
影响因子：
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通讯作者：
Weigu Li;J. Llibre;Xiang Zhang
中科院分区：
文献类型：
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作者：
Weigu Li;J. Llibre;Xiang Zhang
本文利用线性算子理论和正规形式，推广了poincar<s:1>[11]关于微分方程组在奇点邻域上局部第一积分不存在的结论。作为推广结果的应用，在更弱的条件下，我们得到了关于半拟齐次系统的局部第一积分的Furta[8]的结果。此外，对于微分同态和周期微分系统，给出了它们的第一积分的定义，并将以前关于微分方程组的结果推广到不动点邻域内的微分同态和常解邻域内的周期微分系统。
In this paper using theory of linear operators and normal forms we generalize a result of Poincaré [11] about the non-existence of local first integrals for systems of differential equations in a neighbourhood of a singular point. As an application of the generalized result, and under more weak conditions we obtain a result of Furta [8] about local first integrals of semi-quasi-homogeneous systems. Moreover, for diffeomorphisms and periodic differential systems we give definitions of their first integrals, and generalize the previous results about systems of differential equations to diffeomorphisms in a neighbourhood of a fixed point and to periodic differential systems in a neighbourhood of a constant solution.