用Painleve分析构造不可积动力系统的特解
Construction of Special Solutions for Nonintegrable Dynamical Systems with the help of the Painleve Analysis
摘要：
考虑了广义Henon-Heiles系统。在两个不可积的情况下，借助Painleve测试，新的特解被发现为Laurent级数，取决于三个参数。所得级数收敛于某个环。其中一个参数决定了奇异点的位置，其他参数决定了级数的系数。对于这些参数的某些值，得到的Laurent级数与已知精确解的Laurent级数一致。Painleve检验不仅可以用来构造局部解作为Laurent级数，而且可以用来寻找椭圆解。
英文摘要：
The generalized Henon-Heiles system has been considered. In two nonintegrable cases with the help of the Painleve test new special solutions have been found as Laurent series, depending on three parameters. The obtained series converge in some ring. One of parameters determines the singularity point location, other parameters determine coefficients of series. For some values of these parameters the obtained Laurent series coincide with the Laurent series of the known exact solutions. The Painleve test can be used not only to construct local solutions as the Laurent series but also to find elliptic solutions.
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