Geodesic flow on SO(4) and the intersection of quadrics.

This note studies the relationship between the complete integrability of geodesic flow on SO(4) with a left-invariant metric and the geometry of the intersection of four quadrics in P(6).

A complete solution of the periodic Toda problem.

The motion of the periodic Toda lattice is explicitly determined in terms of Abelian integrals.

On some periodic toda lattices.

A discrete version of Floquet's theory is developed and applied to a system of non-linear differential equations related to the periodic Toda lattice. A special solution previously found by Toda is thus seen to fit into the formalism of inverse scattering problems.

On some isospectral second order differential operators.

A method of exhibiting potentials which are uniquely determined by their spectra is discussed and illustrated in an example.