  We study over a number field, the iterates of automorphisms of the affine
space. More precisely, we are interested in the periodic and non-periodic
points; for the former the questions are similar to the ones about torsion
points on abelian varieties, for the latter the questions are similar to the
problems on counting rational points on varieties. In order to study this
problem, we define geometric invariants, which are defined thanks to the cone
of divisors associated to some varieties constructed from the automorphisms. We
study, in all dimension, these invariants and bound them above for one of them
we obtain a bound depending on the dynamical degree, this bound is reach by
some automorphisms, in particular this bound is optimal. For an other
invariant, we obtain in all dimension, thanks to a geometrical construction and
under some geometric conditions, a better bound.
