The moduli space of germs of generic families of analytic diffeomorphisms unfolding a parabolic fixed point

We describe the moduli space of germs of generic families of analytic diffeomorphisms which unfold a parabolic fixed point of codimension 1. A complete modulus is given by unfolding the Ecalle-Voronin modulus over a sector of opening greater than 2 pi in the canonical parameter E. In the region of overlap (Glutsyuk sector of parameter space) where the two fixed points are connected by orbits, we identify the necessary compatibility between the two representatives of the modulus. The compatibility condition implies the existence of a normalization for which the modulus is 1/2-summable in epsilon, non-summability occurring in the direction of real multipliers of the fixed points. We show that the compatibility condition together with the summability is sufficient for realization of the modulus.