  We show that, for every compact n-dimensional manifold, n\geq 1, there is a
residual subset of Diff^1(M) of diffeomorphisms for which the homoclinic class
of any periodic saddle of f verifies one of the following two possibilities:
Either it is contained in the closure of an infinite set of sinks or sources
(Newhouse phenomenon), or it presents some weak form of hyperbolicity called
dominated splitting (this is a generalization of a bidimensional result of Mane
[Ma3}). In particular, we show that any C^1 -robustly transitive diffeomorphism
admits a dominated splitting.
