  In the classical three rotor problem, three equal point masses move on a
circle subject to attractive cosine potentials of strength g. In the center of
mass frame, energy E is the only known conserved quantity. In earlier work
[Krishnaswami and Senapati, arXiv:1810.01317, Oct. 2018, arXiv:1811.05807, Nov.
2018], an order-chaos-order transition was discovered in this system along with
a band of global chaos for 5.33g < E < 5.6g. Here, we provide numerical
evidence for ergodicity and mixing in this band. The distributions of relative
angles and angular momenta along generic trajectories are shown to approach the
corresponding distributions over constant energy hypersurfaces (weighted by the
Liouville measure) as a power-law in time. Moreover, trajectories emanating
from a small volume are shown to become uniformly distributed over constant
energy hypersurfaces, indicating that the dynamics is mixing. Outside this
band, ergodicity and mixing fail, though the distributions of angular momenta
over constant energy hypersurfaces show interesting phase transitions from
Wignerian to bimodal with increasing energy. Finally, in the band of global
chaos, the distribution of recurrence times to finite size cells is found to
follow an exponential law with the mean recurrence time satisfying a scaling
law involving an exponent consistent with global chaos and ergodicity.
