Normalization of strongly hyperbolic logarithmic transseries and complex Dulac germs

We give normal forms for strongly hyperbolic logarithmic transseries f = z^r + ... (r is a positive real number nonequal to 1), with respect to parabolic logarithmic normalizations. These normalizations are obtained using fixed point theorems, and are given algorithmically, as limits of Picard sequences in appropriate formal topologies. The results are applied to describe the supports of normalizations and to prove that the strongly hyperbolic complex Dulac germs are analytically normalizable on standard quadratic domains inside the class of complex Dulac germs.