  We prove that the category of ordered abelian groups equipped with an
automorphism has the Amalgamation Property, deduce that their inductive theory
is NIP in the sense of positive logic, and initiate a development of the latter
framework.
  As byproducts of the proof, we obtain a generalised version of the Hahn
Embedding Theorem which allows to lift each automorphism of an ordered abelian
group to one of an ordered real vector space, and we show that, on
existentially closed structures, linear combinations of iterates of the
automorphism have the Intermediate Value Property.
