Modulus of analytic classification for unfoldings of generic parabolic diffeomorphisms

In this paper we give a complete modulus of analytic classification under weak equivalence for generic analytic 1-parameter unfoldings of diffeomorphisms with a generic parabolic point. The modulus is composed of a canonical parameter associated to the family, together with an unfolding of the Ecalle–Voronin modulus. We then study the fixed points bifurcating from a parabolic point with nontrivial Ecalle–Voronin modulus and show that some of the non-hyperbolic resonant ones are non integrable.
In the Addendum it is shown that weak equivalence can be replaced by conjugacy.