An iterated function system for the closure of the adding machine group
Fractals, cilt.23, sa.3, 2015 (SCI-Expanded, Scopus)
- 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.