  Context. Photometric monitoring of the variability of brown dwarfs can
provide useful information about the structure of clouds in their cold
atmospheres. The brown-dwarf binary system Luhman 16AB is an interesting target
for such a study, as its components stand at the L/T transition and show high
levels of variability. Luhman 16AB is also the third closest system to the
Solar system, allowing precise astrometric investigations with ground-based
facilities. Aims. The aim of the work is to estimate the rotation period and
study the astrometric motion of both components. Methods. We have monitored
Luhman 16AB over a period of two years with the lucky-imaging camera mounted on
the Danish 1.54m telescope at La Silla, through a special i+z long-pass filter,
which allowed us to clearly resolve the two brown dwarfs into single objects.
An intense monitoring of the target was also performed over 16 nights, in which
we observed a peak-to-peak variability of 0.20 \pm 0.02 mag and 0.34 \pm 0.02
mag for Luhman 16A and 16B, respectively. Results. We used the 16-night
time-series data to estimate the rotation period of the two components. We
found that Luhman 16B rotates with a period of 5.1 \pm 0.1 hr, in very good
agreement with previous measurements. For Luhman 16A, we report that it rotates
slower than its companion and, even though we were not able to get a robust
determination, our data indicate a rotation period of roughly 8 hr. This
implies that the rotation axes of the two components are well aligned and
suggests a scenario in which the two objects underwent the same accretion
process. The 2-year complete dataset was used to study the astrometric motion
of Luhman 16AB. We predict a motion of the system that is not consistent with a
previous estimate based on two months of monitoring, but cannot confirm or
refute the presence of additional planetary-mass bodies in the system.
