  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.
