Abstract:
The two-parameter family of
bifurcation diagrams $\Sigma$ of the moment map is investigated in
the integrable Kovalevskaya-Yehia case for the motion of a rigid body.
A method is developed which is useful for calculating the bifurcation set $\Theta$
in the parameter space which corresponds to
bifurcations of diagrams in $\Sigma$
and for classifying these bifurcations.
The properties of the sets
$\Sigma$ and $\Theta$ are thoroughly investigated, and details of
the modifications
the bifurcation diagrams undergo as the value of the parameter
crosses $\Theta$ are described. Illustrations which explain the
structure of the different types of diagram and their interrelations are given.
Bibliography: 22 titles.