Geodesic
Saddle singularities of complexity $1$ of integrable Hamiltonian systems
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2011), pp. 10-20

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Properties of saddle singularities of rank $0$ and complexity $1$ for integrable Hamiltonian systems are studied. An invariant ($f_n$-graph) solving the problem of semi-local classification of saddle singularities of rank $0$ for an arbitrary complexity was constructed earlier by the author. In this paper, a more simple form of the invariant for singularities of complexity $1$ is obtained and some properties of such singularities are described in algebraic terms. In addition, the paper contains a list of saddle singularities of complexity $1$ for systems with three degrees of freedom. 
@article{VMUMM_2011_2_a1,
     author = {A. A. Oshemkov},
     title = {Saddle singularities of complexity $1$ of integrable {Hamiltonian} systems},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {10--20},
     publisher = {mathdoc},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2011_2_a1/}
}
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A. A. Oshemkov. Saddle singularities of complexity $1$ of integrable Hamiltonian systems. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2011), pp. 10-20. http://geodesic.mathdoc.fr/item/VMUMM_2011_2_a1/