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.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 1, pp. 122–140, January, 1997.
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Samoilenko, A.M., Parasyuk, I.O. Nilpotent flows of S1-invariant Hamiltonian systems on 4-dimensional symplectic manifolds. Ukr Math J 49, 135–155 (1997). https://doi.org/10.1007/BF02486622
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DOI: https://doi.org/10.1007/BF02486622