The Completely Integrable Differential Systems are Essentially Linear Differential Systems
The Completely Integrable Differential Systems are Essentially Linear Differential Systems
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DOI：
10.1007/s00332-015-9243-z
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发表时间：
2015-03
影响因子：
3
通讯作者：
J. Llibre;C. Valls;Xiang Zhang
中科院分区：
文献类型：
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作者：
J. Llibre;C. Valls;Xiang Zhang
的开子集中定义一个自治微分系统。假设系统是完全可积的，即存在函数无关的一类第一积分。正如我们将看到的，我们可以在不丧失一般性的情况下假设系统的散度在勒贝格测度的完整子集中不为零。那么，任何雅可比乘子函数与第一个积分无关。此外，系统的轨道等效于线性微分系统的完整勒贝格测量子集。此外，对于可积多项式微分系统，我们刻画了它们的雅可比乘子类型。
Letbe aautonomous differential system withdefined in an open subsetof. Assume that the systemiscompletely integrable, i.e., there existfunctionally independent first integrals of classwith. As we shall see, we can assume without loss of generality that the divergence of the systemis not zero in a full Lebesgue measure subset of. Then, any Jacobian multiplier is functionally independent of thefirst integrals. Moreover, the systemisorbitally equivalent to the linear differential systemin a full Lebesgue measure subset of. Additionally, for integrable polynomial differential systems, we characterize their type of Jacobian multipliers.