Classification of saddle-focus singularities
Differential Geometry
2023-01-26 v1 Symplectic Geometry
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 semi-local 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 the constructed algorithm, a complete list of singularities of saddle-focus type of complexity , , and , i.e., singularities whose leaf contains one, two, or three singular points of rank , is obtained. Earlier both singularities of saddle-focus type of complexity were also described by L.M. Lerman.
Cite
@article{arxiv.2301.10298,
title = {Classification of saddle-focus singularities},
author = {I. K. Kozlov and A. A. Oshemkov},
journal= {arXiv preprint arXiv:2301.10298},
year = {2023}
}