Abstract. Holomorphic functions with neutral fixed points often generate delicate dynamical problems, especially when the derivative is not a root of unity. We consider them as a perturbation of parabolic ones (i.e. fixed point whose derivative is a root of unity). We are naturally lead to the study of "Parabolic renormalization." In a joint work with Hiroyuki Inou, we found a concrete class of functions which is invariant under this renormalization. This result was used by Buff and Cheritat to prove the existence of a quadratic polynomial whose Julia set has positive Lebesgue measure.