Abstract & Overview
The topology of the Liouville foliation in the phase space of the Kovalevskaya top is completely characterized. It involves ve distinct families of tori which are separated by 14 types of bifurcations. The bifurcations are organized by 13 dierent singularities, six of which are relative equilibria, and seven degenerate critical orbits. The bare molecules for the ten types of isoenergy surfaces have been determined earlier, but important information about the connection between admissible coordinate systems at dierent bifurcations has been missing so far. This gap is lled with the computation of marked molecules, based on a new method which uses molecules corresponding to loops around singular points in the bifurcation diagram. A global set of admissible coordinates is identied, and the molecules of all isoenergy surfaces are endowed with gluing matrices and topological marks.