  A point q in a contact manifold is called a translated point for a
contactomorphism \phi, with respect to some fixed contact form, if \phi(q) and
q belong to the same Reeb orbit and the contact form is preserved at q. In this
article we discuss a version of the Arnold conjecture for translated points of
contactomorphisms and, using generating functions techniques, we prove it in
the case of spheres (under a genericity assumption) and projective spaces.
