  In the scope of the star formation process, it is unclear how the environment
shapes the initial mass function (IMF). While observations of open clusters
propose a universal picture for the IMF from the substellar domain up to a few
solar masses, the young association eta Chamaeleontis presents an apparent lack
of low mass objects (m<0.1 Msun). Another unusual feature of this cluster is
the absence of wide binaries with a separation > 50 AU. We aim to test whether
dynamical evolution alone can reproduce the peculiar properties of the
association assuming a universal IMF. We use a pure N-body code to simulate the
dynamical evolution of the cluster for 10 Myr, and compare the results with
observations. A wide range of values for the initial parameters are tested in
order to identify the initial state that would most likely lead to
observations. In this context we also investigate the influence of the initial
binary population on the dynamics and the possibility of having a discontinuous
single IMF near the transition to the brown dwarf regime. We consider as an
extreme case an IMF with no low mass systems (m<0.1 Msun). The initial
configurations cover a wide range of initial density, from 10^2 to 10^8
stars/pc^3, in virialized, hot and cold dynamical state. We do not find any
initial state that would evolve from a universal single IMF to fit the
observations. Only when starting with a truncated IMF without any very low mass
systems and no wide binaries, can we reproduce the cluster core properties with
a success rate of 10% at best. Pure dynamical evolution alone cannot explain
the observed properties of eta Cha from universal initial conditions. The lack
of brown dwarfs and very low mass stars, and the peculiar binary properties
(low binary fraction and lack of wide binaries), are probably the result of the
star formation process in this association. (abridged)
