Context : 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 \text { M } _ { \odot } ) .
Another unusual feature of this cluster is the absence of wide binaries with a separation > 50 AU .

Aims : We aim to test whether dynamical evolution alone can reproduce the peculiar properties of the association under the assumption of a universal IMF .

Methods : 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 ( number of systems , typical radius of the density distribution and virial ratio ) 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 \text { M } _ { \odot } ) .

Results : The initial configurations cover a wide range of initial density , from 10 ^ { 2 } to 10 ^ { 8 } stars/ \text { 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 .

Conclusions : Pure dynamical evolution alone can not explain the observed properties of \eta Chamaeleontis 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 .