A Thompson group for the basilica

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.

Published version

References in corpus (2)

• Higher Dimensional Thompson Groups
• The Algebra of Strand Splitting. I. A Braided Version of Thompson's Group V

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• Rational Gluing in Edge Replacement Systems
• On Thompson Groups for Ważewski Dendrites