  In this short note, we give a sketch of a new proof of the exponential
contraction of the Feigenbaum renormalization operator in the hybrid class of
the Feigenbaum fixed point. The proof uses the non existence of invariant line
fields in the Feigenbaum tower (C. McMullen), the topological convergence (D.
Sullivan), and a new infinitesimal argument, different from previous methods by
C. McMullen and M. Lyubich. The method is very general: for instance, it can be
used in the classical renormalization operator and in the Fibonacci
renormalization operator.
