  We describe the asymptotic behavior as time goes to infinity of solutions of
the 2 dimensional corotational wave map system and of solutions to the 4
dimensional, radially symmetric Yang-Mills equation, in the critical energy
space, with data of energy smaller than or equal to a harmonic map of minimal
energy. An alternative holds: either the data is the harmonic map and the
soltuion is constant in time, or the solution scatters in infinite time.
