  We investigate the dynamics of axion-like particle (ALP) dark matter where
the field range is enlarged by a monodromy. The monodromy potential allows
sufficient production of dark matter also at larger couplings to the Standard
Model particles. The potential typically features a number of "wiggles" that
lead to a rapid growth of fluctuations. Using classical-statistical field
theory simulations we go beyond the linear regime and treat the system in the
non-linear and even non-perturbative regime. For sufficiently strong wiggles
the initially homogeneous field is completely converted into fluctuations. The
fluctuations correspond to dark matter particles with a non-vanishing velocity
and we consider the corresponding restrictions from structure formation as well
as the effects on today's dark matter density. Since all the dark matter is
made up from these strong fluctuations, the dark matter density features large,
$\mathcal{O}(1)$ fluctuations at scales $\lesssim 10^{6}\,{\rm km}\sqrt{{\rm
eV}/m_a}$.
