| Abstract: | We prove that if a complex Hamiltonian system withn degrees of freedom hasn functionally independent meromorphic first integrals in involution and the monodromy group of the corresponding variational
system along some phase curve hasn pairwise skew-orthogonal two-dimensional invariant subspaces, then the restriction of the action of this group to each to
these subspaces has a rational first integral. The result thus obtained is applied to natural mechanical systems with homogeneous
potential, in particular, to then-body problem.
Supported by the program “Leading Scientific Schools,” RFBR grant No. 00-15-96146.
Institute of Radiotechnics and Electronics, Russian Academy of Sciences. Translated from Funktsional'nyi Analiz i Ego Prilozheniya,
Vol. 34, No. 3, pp. 26–36, July–September, 2000.
Translated by A. I. Shtern |
