Geodesic
Classification of saddle-focus singularities
Čebyševskij sbornik, Tome 21 (2020) no. 2, pp. 228-243

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The paper presents an algorithm for topological classification of nondegenerate saddle-focus singularities of integrable Hamiltonian systems with three degrees of freedom up to semilocal equivalence. In particular, we prove that any singularity of saddle-focus type can be represented as an almost direct product in which the acting group is cyclic. Based on constructed algorithm, a complete list of singularities of saddle-focus type of complexity 1, 2, and 3, i. e., singularities whose leaf contains one, two, or three singular points of rank 0, is obtained. Earlier, both singularities of saddle-focus type of complexity 1 were also described by L. M. Lerman.
Keywords: integrable system, Liouville foliation, saddle-focus singularity. 
@article{CHEB_2020_21_2_a16,
     author = {I. K. Kozlov and A. A. Oshemkov},
     title = {Classification of saddle-focus singularities},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {228--243},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2020_21_2_a16/}
}
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I. K. Kozlov; A. A. Oshemkov. Classification of saddle-focus singularities. Čebyševskij sbornik, Tome 21 (2020) no. 2, pp. 228-243. http://geodesic.mathdoc.fr/item/CHEB_2020_21_2_a16/