A self-similar group in the sense of iterated function system

DEMİR B., SALTAN M.

Far East Journal of Mathematical Sciences, vol.60, no.1, pp.83-99, 2012 (Scopus) identifier

  • 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.