  We study the thermalization process in highly occupied non-Abelian plasmas at
weak coupling. The non-equilibrium dynamics of such systems is classical in
nature and can be simulated with real-time lattice gauge theory techniques. We
provide a detailed discussion of this framework and elaborate on the results
reported in~\cite{Berges:2013eia} along with novel findings. We demonstrate the
emergence of universal attractor solutions, which govern the non-equilibrium
evolution on large time scales both for non-expanding and expanding non-Abelian
plasmas. The turbulent attractor for a non-expanding plasma drives the system
close to thermal equilibrium on a time scale $t\sim Q^{-1} \alpha_s^{-7/4}$.
The attractor solution for an expanding non-Abelian plasma leads to a strongly
interacting albeit highly anisotropic system at the transition to the
low-occupancy or quantum regime. This evolution in the classical regime is,
within the uncertainties of our simulations, consistent with the ``bottom up''
thermalization scenario~\cite{Baier:2000sb}. While the focus of this paper is
to understand the non-equilibrium dynamics in weak coupling asymptotics, we
also discuss the relevance of our results for larger couplings in the early
time dynamics of heavy ion collision experiments.
