مشخصات پژوهش

In the qualitative study of integrable Hamiltonian systems, an important characteristic is the topological type of isoenergetic surfaces. The general topological classification of isoenergetic 3-surfaces was constructed by Fomenko in [7] and by Fomenko and Zieschang in [8]. The topology of isoenergetic surfaces has been studied by many authors for classical cases of integrability (see, e.g., [1]). In particular, in [3, 5], a number of methods for studying isoenergetic surfaces for problems of mechanics were developed. Such problems are described by the Euler equations on the Lie algebra e (3) . These methods do not generally apply to the Lie algebra so (4) . In this paper, we suggest a method for studying the topology of isoenergetic surfaces on so (4) that is based on an idea of A.A. Oshemkov. We apply this method to solving the problem for an integrable case that has recently been discovered by Sokolov [4].