Geodesic
Topological classification of Hamiltonian systems on two-dimensional noncompact manifolds
Sbornik. Mathematics, Tome 211 (2020) no. 8, pp. 1127-1158

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We construct a complete topological invariant of foliations of finite type defined by smooth functions on two-dimensional noncompact orientable manifolds. In particular, we describe a complete topological classification of noncompact bifurcations of such foliations. We establish a natural one-to-one correspondence between the set of all such bifurcations and the set of oriented coloured graphs of a special form. As a consequence, we obtain the Liouville and trajectory classifications of Hamiltonian systems of finite type on noncompact two-dimensional manifolds. Bibliography: 25 titles.
Keywords: Hamiltonian system, topological classification, trajectory equivalence, noncompact atom, $f$-graph. 
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     author = {S. S. Nikolaenko},
     title = {Topological classification of {Hamiltonian} systems on two-dimensional noncompact manifolds},
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     url = {http://geodesic.mathdoc.fr/item/SM_2020_211_8_a2/}
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S. S. Nikolaenko. Topological classification of Hamiltonian systems on two-dimensional noncompact manifolds. Sbornik. Mathematics, Tome 211 (2020) no. 8, pp. 1127-1158. http://geodesic.mathdoc.fr/item/SM_2020_211_8_a2/