HackerPapers

arXiv:1201.4225math.GR

A Thompson group for the basilica

James Belk, Bradley Forrest

Early discovery. Linked by one identifiable commenter. This paper is outside the main ranking; a mention is not an endorsement.

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.

arXiv comments
Published version
Journal reference
Group. Geom. Dynam. 9.4 (2015) 975-1000
DOI
doi:10.4171/GGD/333
Subjects
math.GRGroup Theory math.DSDynamical Systems

On Hacker News

Linked by 1 identifiable commenter in 1 comment across 1 thread, from Aug 2015 to Aug 2015.

Comments linking this paper, per year.

Discussed in comments1 thread

  1. How to Fold a Julia Fractal 1 comment

    • There's not a whole lot of material about the Julia set itself. When he talks about "folding" the Julia set, I immediately thought of this picture of some fractions http://i.imgur.com/wxz2a3t.png from this paper: http://arxiv.org/abs/1201.4225v1

      mrcactu5View on HNParent context

Submitted to Hacker News

Connected through shared HN threads, not inferred similarity or a recommendation.