  This thesis deals with automorphisms of real algebraic surfaces, which are
polynomial transformations with a polynomial inverse. The main concern is
whether their restriction to the real locus reflects all the richness of the
complex dynamics. This question is declined in two directions: the topological
entropy and the Fatou set.
  For the first one, we introduce a purely geometric quantity depending only on
the surface, and we call it concordance. Then we show that the ratio of real
and complex entropies is linked to this quantity. The concordance is
explicitely computed for many examples of surfaces, especially abelian surfaces
which are broadly studied, as well as some K3 surfaces.
  In the second part, we are interested in the Fatou set, which corresponds to
complex points for which the dynamics is simple. Thanks to previous results of
Dinh and Sibony about closed positive currents, we prove that this set is
hyperbolic in the sense of Kobayashi, after possibly deleting some curves which
are fixed by (an iterate of) our transformation. From this property we deduce
that, except for some exceptional cases in which the topology of the real locus
is simple and the dynamics well understood, this real locus cannot be entirely
contained in the Fatou set. Thus the complexity of the dynamics is observable
on real points in most cases.
