Abstract
This paper is a sequel to Part I [13] and Part II [14,15]. In the current article we relate several combinatorial descriptions of the Julia sets for hyperbolic polynomial diffeomorphisms of C2: quotients of solenoids [3], automata [22] and Hubbard trees [14,15]. The notion of iterated monodromy groups are defined for such diffeomorphisms and are used to construct automata from Hubbard trees.
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