On Julia sets of postcritically finite branched coverings Part I--coding of Julia sets

Abstract

We define Julia sets for (topological) expanding postcritically finite branched coverings on $S^2$, and show the existence and the uniqueness of Julia sets. Our main aim is the investigation of codings of Julia sets (i.e. semiconjugacies between symbolic dynamics and Julia sets). In particular, it is proved that if two expanding branched coverings are combinatorially equivalent, then their Julia sets are topologically conjugate.