TY - JOUR
T1 - Hyperbolic polynomial diffeomorphisms of C2. III
T2 - Iterated monodromy groups
AU - Ishii, Yutaka
PY - 2014/4/1
Y1 - 2014/4/1
N2 - 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.
AB - 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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U2 - 10.1016/j.aim.2013.12.031
DO - 10.1016/j.aim.2013.12.031
M3 - Article
AN - SCOPUS:84893111219
SN - 0001-8708
VL - 255
SP - 242
EP - 304
JO - Advances in Mathematics
JF - Advances in Mathematics
ER -