  We introduce a notion of weak Denjoy subsystem (WDS) that generalizes the
Aubry-Mather Cantor sets to diffeomorphisms of manifolds. We explain how a
rotation number can be associated to such a WDS. Then we build in any horseshoe
a continuous one parameter family of such WDS that is indexed by its rotation
number. Looking at the inverse problem in the setting of Aubry-Mather theory,
we also prove that for a generic conservative twist map of the annulus, the
majority of the Aubry-Mather sets are contained in some horseshoe that is
associated to a Aubry-Mather set with a rational rotation number.
