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

SALTAN M., DEMİR B.

Fractals, cilt.23, sa.3, 2015 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 23 Sayı: 3
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1142/s0218348x15500334
  • Dergi Adı: Fractals
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: p-ary Adding Machine, Automorphism Group, Fixed-Point Theorem, Iterated Function System
  • Anadolu Üniversitesi Adresli: Evet

Özet

© 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.