Geometrical aspects of Ziglin's non-integrability theorem for complex Hamiltonian systems (Q1113147)

The classical approach, namely the series representation of solutions, is applied to obtain the generators for the monodromy group of complex Hamiltonian systems. Two other ways are discussed as well. The complex linear differential equations are regarded as holomorphic connections on holomorphic vector bundles over Riemann surfaces. The special attention is paid, with respect to \textit{S. L. Ziglin}'s Non-integrability Theorem [Funct. Anal. Appl. 16, 181-189 (1983); translation from Funkts. Anal. Prilozh. 16, No.3, 30-41 (1982; Zbl 0524.58015)], to the computation of a monodromy group to the hypergeometric equation.