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 Ori OB1b 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 4 h up to 100 h , 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 2 h and 4 h , 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 . Table 2 is only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr ( 130.79.128.5 ) or via http : //cdsweb.u-strasbg.fr/cgi-bin/qcat ? J/A+A/