Geodesic
The symmetry groups of bifurcations of integrable Hamiltonian systems
Sbornik. Mathematics, Tome 205 (2014) no. 11, pp. 1668-1682

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Two-dimensional atoms are investigated; these are used to code bifurcations of the Liouville foliations of nondegenerate integrable Hamiltonian systems. To be precise, the symmetry groups of atoms with complexity at most 3 are under study. Atoms with symmetry group $\mathbb Z_p\oplus\mathbb Z_q$ are considered. It is proved that $\mathbb Z_p\oplus\mathbb Z_q$ is the symmetry group of a toric atom. The symmetry groups of all nonorientable atoms with complexity at most 3 are calculated. The concept of a geodesic atom is introduced. Bibliography: 9 titles.
Keywords: integrable systems, atoms, finite groups. 
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     author = {E. I. Orlova},
     title = {The symmetry groups of bifurcations of integrable {Hamiltonian} systems},
     journal = {Sbornik. Mathematics},
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     publisher = {mathdoc},
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     number = {11},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2014_205_11_a5/}
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E. I. Orlova. The symmetry groups of bifurcations of integrable Hamiltonian systems. Sbornik. Mathematics, Tome 205 (2014) no. 11, pp. 1668-1682. http://geodesic.mathdoc.fr/item/SM_2014_205_11_a5/