A Thompson group for the basilica
Group Theory
2023-10-18 v2 Dynamical Systems
Abstract
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 diagrams for this group which we call arc pair diagrams, and we use these diagrams to prove that the group is finitely generated. We also prove that the group is virtually simple.
Keywords
Cite
@article{arxiv.1201.4225,
title = {A Thompson group for the basilica},
author = {James Belk and Bradley Forrest},
journal= {arXiv preprint arXiv:1201.4225},
year = {2023}
}
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