  Space and astrophysical plasmas are frequently found in the regime of
differential rotation, where the presence of a magnetic field can result in the
magnetorotational instability, directly responsible for important phenomena
such as turbulent angular momentum transport in accretion disks. In the absence
of an imposed magnetic field, a nonlinear dynamo is necessary for this
transport mechanism to take place. In protoplanetary disks there are regions
with high density and very low temperatures, which are two necessary conditions
for the Hall effect to operate, affecting the development of the dynamo and the
associated turbulence. In this work we perform local magnetohydrodynamic (MHD)
simulations to study transition to weak turbulence in Keplerian shear flows
with Hall effect. The Hall effect is shown to lead the system to long-lived
turbulent transients whose decay time follows an exponential dependence on the
magnetic Reynolds number and the Hall parameter.
