2017
Том 69
№ 6

All Issues

Nilpotent flows of S1-invariant Hamiltonian systems on 4-dimensional symplectic manifolds

Parasyuk I. O., Samoilenko A. M.

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Abstract

We investigate S1-invariant Hamiltonian systems on compact 4-dimensional symplectic manifolds with free symplectic action of a circle. We show that, in a rather general case, such systems generate ergodic flows of types (quasiperiodic and nilpotent) on their isoenergetic surfaces. We solve the problem of straightening of these flows.

English version (Springer): Ukrainian Mathematical Journal 49 (1997), no. 1, pp 135-155.

Citation Example: Parasyuk I. O., Samoilenko A. M. Nilpotent flows of S1-invariant Hamiltonian systems on 4-dimensional symplectic manifolds // Ukr. Mat. Zh. - 1997. - 49, № 1. - pp. 122–140.

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