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.