Bifurcation sets in the Kovalevskaya-Yehia problem

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.
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