  We introduce the notion of a twisted differential operator of given radius
relative to an endomorphism $$\sigma$$ of an affinoid algebra A. We show that
this notion is essentially independent of the choice of the endomorphism
$$\sigma$$. As a particular case, we obtain an explicit equivalence between
modules endowed with a usual integrable connection (i.e. differential systems)
and modules endowed with a $$\sigma$$-connection of the same radius (i.e.
q-difference systems). Moreover, this equivalence preserves cohomology and in
particular solutions.
