Classification of four-dimensional integrable Hamiltonian systems and Poisson actions of
Sbornik. Mathematics, Tome 78 (1994) no. 2, pp. 479-506

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Integrable Hamiltonian systems and Poisson actions of the group $\mathbb{R}^2$ with simple singular points on a smooth ($C^\infty$ or real-analytic) four-dimensional symplectic manifold $(M,\Omega)$ are studied, where $\Omega$ is a symplectic 2-form.
@article{SM_1994_78_2_a12,
     author = {L. M. Lerman and Ya. L. Umanskii},
     title = {Classification of four-dimensional integrable {Hamiltonian} systems and {Poisson} actions of},
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L. M. Lerman; Ya. L. Umanskii. Classification of four-dimensional integrable Hamiltonian systems and Poisson actions of. Sbornik. Mathematics, Tome 78 (1994) no. 2, pp. 479-506. http://geodesic.mathdoc.fr/item/SM_1994_78_2_a12/