  We consider the Cauchy problem for a spherically symmetric SU(2) Yang-Mills
field propagating outside the Schwarzschild black hole. Although solutions
starting from smooth finite energy initial data remain smooth for all times,
not all of them scatter since there are non-generic solutions which
asymptotically tend to unstable static solutions. We show that a static
solution with one unstable mode appears as an intermediate attractor in the
evolution of initial data near a border between basins of attraction of two
different vacuum states. We study the saddle-point dynamics near this
attractor, in particular we identify the universal phases of evolution: the
ringdown approach, the exponential departure, and the eventual decay to one of
the vacuum states.
