  We explore the rotation and activity of very low mass (VLM) objects by means
of a photometric variability study. Our targets in the vicinity of Epsilon Ori
belong to the OriOB1b population in the Orion star-forming complex. In this
region we selected 143 VLM stars and brown dwarfs (BDs), whose photometry in
RIJHK is consistent with membership of the young population. The variability of
these objects was investigated using a densely sampled I-band time series
covering four consecutive nights with altogether 129 data points per object.
Our targets show three types of variability: Thirty objects, including nine
BDs, show significant photometric periods, ranging from 4h up to 100h, which we
interpret as the rotation periods. Five objects, including two BDs, exhibit
variability with high amplitudes up to 1 mag which is at least partly
irregular. This behaviour is most likely caused by ongoing accretion and
confirms that VLM objects undergo a T Tauri phase similar to solar-mass stars.
Finally, one VLM star shows a strong flare event of 0.3 mag amplitude. The
rotation periods show dependence on mass, i.e. the average period decreases
with decreasing object mass, consistent with previously found mass-period
relationships in younger and older clusters. The period distribution of BDs
extends down to the breakup period, where centrifugal and gravitational forces
are balanced. Combining our BD periods with literature data, we found that the
lower period limit for substellar objects lies between 2h and 4h, more or less
independent of age. Contrary to stars, these fast rotating BDs seem to evolve
at constant rotation period from ages of 3 Myr to 1 Gyr, in spite of the
contraction process. Thus, they should experience strong rotational braking.
