An iterated function system for the closure of the adding machine group

SALTAN M., DEMİR B.

Fractals, vol.23, no.3, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 23 Issue: 3
  • Publication Date: 2015
  • Doi Number: 10.1142/s0218348x15500334
  • Journal Name: Fractals
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: p-ary Adding Machine, Automorphism Group, Fixed-Point Theorem, Iterated Function System
  • Anadolu University Affiliated: Yes

Abstract

© 2015 World Scientific Publishing Company.In this paper, first we equip the automorphism group of the p-ary rooted tree X∗with a natural metric and define a family of contractions on Aut(X∗). Then, we construct an iterated function system (IFS) whose attractor is the closure of the adding machine group on Aut(X∗). Finally, we show that this group is a strong self-similar group in the sense of IFS.