Classification of nondegenerate equilibria and degenerate 1-dimensional orbits of the Kovalevskaya-Yehia integrable system

Abstract

The paper is devoted to a topological analysis of the Kovalevskaya-Yehia integrable case in rigid body dynamics. It is proved that the integral has the Bott property on isoenergy surfaces of the system; the topology of the Liouville foliation in a neighbourhood of degenerate 1-dimensional orbits and equilibria (points of rank 0) is also described. In particular, marked loop molecules are constructed for degenerate 1-dimensional orbits, and a representation in the form of an almost direct product is found for nondegenerate singularities of rank 0.Bibliography: 17 titles.