We continue the study of noninvertible topological dynamical systems with expanding behavior. We introduce the class of finite type systems which are characterized by the condition that, up to rescaling and uniformly bounded distortion, there are only finitely many iterates. We show that subhyperbolic rational maps and finite subdivision rules (in the sense of Cannon, Floyd, Kenyon, and Parry) with bounded valence and mesh going to zero are of finite type. In addition, we show that the limit dynamical system associated to a selfsimilar, contracting, recurrent, level-transitive group action (in the sense of V. Nekrashevych) is of finite type. The proof makes essential use of an analog of the finiteness of cone types property enjoyed by hyperbolic groups.
1
Université Paul Sabatier, Toulouse, France
2
Indiana University, Bloomington, USA
Peter Haïssinsky; Kevin M. Pilgrim. Finite type coarse expanding conformal dynamics. Groups, geometry, and dynamics, Tome 5 (2011) no. 3, pp. 603-661. doi: 10.4171/ggd/141
@article{10_4171_ggd_141,
author = {Peter Ha{\"\i}ssinsky and Kevin M. Pilgrim},
title = {Finite type coarse expanding conformal dynamics},
journal = {Groups, geometry, and dynamics},
pages = {603--661},
year = {2011},
volume = {5},
number = {3},
doi = {10.4171/ggd/141},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/141/}
}
TY - JOUR
AU - Peter Haïssinsky
AU - Kevin M. Pilgrim
TI - Finite type coarse expanding conformal dynamics
JO - Groups, geometry, and dynamics
PY - 2011
SP - 603
EP - 661
VL - 5
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/141/
DO - 10.4171/ggd/141
ID - 10_4171_ggd_141
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%0 Journal Article
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%A Kevin M. Pilgrim
%T Finite type coarse expanding conformal dynamics
%J Groups, geometry, and dynamics
%D 2011
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%N 3
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/141/
%R 10.4171/ggd/141
%F 10_4171_ggd_141
