Construction of special solutions for nonintegrable dynamical systems with the help of the Painleve analysis

Abstract:
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. One of parameters determines a location of the singularity point, 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 analysis assists to find
solutions in the analytical form as well. For the Henon-Heiles system new two-parameter solutions have been found in terms of the Jacobi elliptic functions.