Classification of saddle-focus singularities

Abstract

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.