Hyperbolic polynomial diffeomorphisms of C2. III: Iterated monodromy groups

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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.

Original languageEnglish
Pages (from-to)242-304
Number of pages63
JournalAdvances in Mathematics
Volume255
DOIs
Publication statusPublished - Apr 1 2014

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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