  In this article we consider large energy wave maps in dimension 2+1, as in
the resolution of the threshold conjecture by Sterbenz and Tataru, but more
specifically into the unit Euclidean sphere, and study further the dynamics of
the sequence of wave maps that are obtained by Sterbenz and Tataru after the
final rescaling at a first, finite or infinite, time singularity. We prove
that, on a suitably chosen sequence of time slices at this scaling, there is a
decomposition of the map, up to an error with asymptotically vanishing energy,
into a decoupled sum of rescaled solitons concentrating in the interior of the
light cone and a term having asymptotically vanishing energy dispersion norm,
concentrating on the null boundary and converging to a constant locally in the
interior of the cone, in the energy space.
