  Our main goal is to study the formation of rocky planets and the first
$100~\textrm{Myr}$ of their dynamical evolution around a star with mass $0.08
M_\odot$ close to the substellar mass limit. We developed two sets of $N$-body
simulations assuming an embryo population affected by tidal and general
relativistic effects refined by the inclusion of the spin-up and contraction of
the central star, and immerse in a gas disk during the first 10 Myr. Each set
of simulations incorporates a different prescription from literature to
calculate the interaction between the gas-disk and the embryos: one widely used
prescription based on results from hydrodynamics simulations, and a recent
prescription based on the analytic treatment of dynamical friction. We found
that given a standard disk model, the dynamical evolution and the final
architectures of the resulting rocky planets is strongly related with the
prescription used to treat the interaction within the gas and the embryos,
having a big impact on the resulting close-in planet population and
particularly on those located inside the habitable zone. We found a good
agreement within the distribution of period ratio of adjacent confirmed
exoplanets observed around very low mass stars and brown dwarfs and those
obtained from our simulations only when the prescription based on dynamical
friction for gas-embryo interaction is used. Our results also reproduce a
close-in planet population of interest located inside the habitable zone. A
fraction of those planets will be exposed for a long period of time to the
stellar irradiation inside the inner edge of the evolving habitable zone until
the zone reaches them.
