微分方程系统不可积性问题研究

Non-integrability of Differential Equation Systems

研究了周期系统Laurent多项式型首次积分和有理首次积分的不存在性问题。利用Floquet理论,证明了如果系统的特征乘数是瓕-非共振的,则系统在平衡点附近不存在Laurent多项式型首次积分。进一步,还在有理函数空间考虑了这一问题,并得到了相应的结果。

The nonexistence of the first integrals of Laurent polynomial and the rational first integrals for periodic systems are considered. Using the Floquet theory, that if the characteristic multipliers of the system are Z - dependent, then the system does not have any nontrivial integral of Laurent polynomial in a neighborhood of a constant solution is proved. Furthermore, the previous conclusion in the rational function space is also considered.