A self-similar group in the sense of iterated function system
Far East Journal of Mathematical Sciences, vol.60, no.1, pp.83-99, 2012 (Scopus)
- Publication Type: Article / Article
- Volume: 60 Issue: 1
- Publication Date: 2012
- Journal Name: Far East Journal of Mathematical Sciences
- Journal Indexes: Scopus
- Page Numbers: pp.83-99
- Keywords: Automorphis m group, Fixed point, Iterated function system, Self-similar group
- Anadolu University Affiliated: Yes
Abstract
In this paper, first we give an iterated function system whose attractor is G m, a subgroup of the automorphism group of an (m + 1) -ary rooted tree. We also show that G m is a self-similar group in the sense of IFS. Then we prove that G m is both isomorphic and isometric to a compact topological group on k-ary Cantor set C k in the case of k = 2m + 1. © 2012 Pushpa Publishing House.