利用Painleve判别法构造广义Henon-Heiles系统的解
Construction of solutions for the generalized Henon-Heiles system with the help of the Painleve test
摘要：
本文考虑了一般形式的Henon-Heiles系统。在不可积的情况下，借助于Painleve检验，新的解被发现为正式的Laurent或Puienix级数，取决于三个参数。其中一个参数决定了奇点的位置，其他参数决定了级数的系数。证明了如果这两个参数的绝对值小于或等于单位，则所得到的级数收敛于某个环。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。
英文摘要：
The Henon-Heiles system in the general form has been considered. In a nonintegrable case with the help of the Painleve test new solutions have been found as formal Laurent or Puiseux series, depending on three parameters. One of parameters determines a location of the singularity point, other parameters determine coefficients of series. It has been proved, that if absolute values of these two parameters are less or equal to unit, then obtained series converge in some ring. For some values of these parameters the obtained Laurent series coincide with the Laurent series of the known exact solutions.
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