Groups, Geometry, and Dynamics
Full-Text PDF (2331 KB) | Metadata | Table of Contents | GGD summary
Published online: 2015-11-16
A Thompson group for the basilicaJames Belk and Bradley Forrest (1) Bard College, Annandale-on-Hudson, USA
(2) The Richard Stockton College of New Jersey, Galloway, USA
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.
Keywords: Tompson’s groups, piecewise-linear homeomorphism, Julia set, invariant lamination
Belk James, Forrest Bradley: A Thompson group for the basilica. Groups Geom. Dyn. 9 (2015), 975-1000. doi: 10.4171/GGD/333