I am reading the paper by Douady and Hubbard, *On the Dynamics of Polynomial-Like Mappings*, and I am at a loss to understand a crucial step in the construction of the right domain for finding the external map to a polynomial-like mapping.

Do you know a reference where the construction of the repeated covering by annuli (in the case $K_f$ is disconnected) is both justified and done in detail?

I have too many doubts to ask a specific closed question about it. Thank you very much.