  Theory and simulations suggest that it is possible to form low-mass
hydrogen-burning stars, brown dwarfs and planetary-mass objects via disc
fragmentation. As disc fragmentation results in the formation of several bodies
at comparable distances to the host star, their orbits are generally unstable.
Here, we study the dynamical evolution of these objects. We set up the initial
conditions based on the outcomes of the SPH simulations of Stamatellos &
Whitworth, and for comparison we also study the evolution of systems resulting
from lower-mass fragmenting discs. We refer to these two sets of simulations as
set 1 and set 2. At 10 Myr, approximately half of the host stars have one
companion left, and approximately 22% (set 1) to 9.8% (set 2) of the host stars
are single. Systems with multiple secondaries in relatively stable
configurations are common (about 30% and 44%, respectively). The majority of
the companions are ejected within 1 Myr with velocities mostly below 5 km/s,
with some runaway escapers with velocities over 30 km/s. About 6% (set 1) and
2% (set 2) of the companions pair up into very low-mass binary systems. The
majority of these pairs escape as very low-mass binaries, while others remain
bound to the host star in hierarchical configurations (often with retrograde
inner orbits). Physical collisions with the host star (0.43 and 0.18 events per
host star for set 1 and set 2) and between companions (0.08 and 0.04 events per
host star for set 1 and set 2) are relatively common and their frequency
increases with increasing disc mass. Our study predicts observable properties
of very low-mass binaries, low-mass hierarchical systems, the brown dwarf
desert, and free-floating brown dwarfs and planetary-mass objects in and near
young stellar groupings, which can be used to distinguish between different
formation scenarios of very low-mass stars, brown dwarfs and planetary-mass
objects.
