  We study the problem of existence of response solutions for a real-analytic
one-dimensional system, consisting of a rotator subjected to a small
quasi-periodic forcing. We prove that at least one response solution always
exists, without any assumption on the forcing besides smallness and
analyticity. This strengthens the results available in the literature, where
generic non-degeneracy conditions are assumed. The proof is based on a
diagrammatic formalism and relies on renormalisation group techniques, which
exploit the formal analogy with problems of quantum field theory; a crucial
role is played by remarkable identities between classes of diagrams.
