Saddle Singularities of Complexity 1 of Integrable Hamiltonian Systems / *Oshemkov A.A.* // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2011. № 2. P. 10-19
[Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 0].

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.

*Key words*:
integrable Hamiltonian systems, momentum mapping,
non-degenerate singularities, topological invariants.