This article is cited in 12 papers

Integrals in Involution for Groups of Linear Symplectic Transformations and Natural Mechanical Systems with Homogeneous Potential

S. L. Ziglin

Kotel'nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences

Abstract: We prove that if a complex Hamiltonian system with $n$ degrees of freedom has $n$ functionally independent meromorphic first integrals in involution and the monodromy group of the corresponding variational system along some phase curve has $n$ pairwise skew-orthogonal two-dimensional invariant subspaces, then the restriction of the action of this group to each of these subspaces has a rational first integral. The result thus obtained is applied to natural mechanical systems with homogeneous potential, in particular, to the $n$-body problem.

UDC: 517.913

Received: 19.03.1999

DOI: 10.4213/faa309

 English version: Functional Analysis and Its Applications, 2000, 34:3, 179–187

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