Geodesic
Classification of hyperbolic singularities of rank zero of integrable Hamiltonian systems
Sbornik. Mathematics, Tome 201 (2010) no. 8, pp. 1153-1191

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A complete invariant is constructed that is a solution of the problem of semilocal classification of saddle singularities of integrable Hamiltonian systems. Namely, a certain combinatorial object (an $f_n$-graph) is associated with every nondegenerate saddle singularity of rank zero; as a result, the problem of semilocal classification of saddle singularities of rank zero is reduced to the problem of enumeration of the $f_n$-graphs. This enables us to describe a simple algorithm for obtaining the lists of saddle singularities of rank zero for a given number of degrees of freedom and a given complexity. Bibliography: 24 titles.
Keywords: integrable Hamiltonian systems, the momentum map, nondegenerate singularities, topological invariants. 
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     author = {A. A. Oshemkov},
     title = {Classification of hyperbolic singularities of rank zero of integrable {Hamiltonian} systems},
     journal = {Sbornik. Mathematics},
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     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2010_201_8_a4/}
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A. A. Oshemkov. Classification of hyperbolic singularities of rank zero of integrable Hamiltonian systems. Sbornik. Mathematics, Tome 201 (2010) no. 8, pp. 1153-1191. http://geodesic.mathdoc.fr/item/SM_2010_201_8_a4/