|
Abstract
|
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].
|