We describe a Thompson-like group of homeomorphisms of the Basilica Julia set. Each element of this group acts as a piecewise-linear homeomorphism of the unit circle that preserves the invariant lamination for the Basilica. We develop an analogue of tree pair that the group is finitely generated. We also prove that the group is virtually simple.
1
Bard College, Annandale-on-Hudson, USA
2
The Richard Stockton College of New Jersey, Galloway, USA
James Belk; Bradley Forrest. A Thompson group for the basilica. Groups, geometry, and dynamics, Tome 9 (2015) no. 4, pp. 975-1000. doi: 10.4171/ggd/333
@article{10_4171_ggd_333,
author = {James Belk and Bradley Forrest},
title = {A {Thompson} group for the basilica},
journal = {Groups, geometry, and dynamics},
pages = {975--1000},
year = {2015},
volume = {9},
number = {4},
doi = {10.4171/ggd/333},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/333/}
}
TY - JOUR
AU - James Belk
AU - Bradley Forrest
TI - A Thompson group for the basilica
JO - Groups, geometry, and dynamics
PY - 2015
SP - 975
EP - 1000
VL - 9
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UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/333/
DO - 10.4171/ggd/333
ID - 10_4171_ggd_333
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%J Groups, geometry, and dynamics
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%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/333/
%R 10.4171/ggd/333
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