An iterated function system for the closure of the adding machine group
Fractals, vol.23, no.3, 2015 (SCI-Expanded, Scopus)
- 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.