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- Title
FROM SELF-SIMILAR STRUCTURES TO SELF-SIMILAR GROUPS.
- Authors
KELLEHER, DANIEL J.; STEINHURST, BENJAMIN A.; WONG, CHUEN-MING M.
- Abstract
We explore the relationship between the limit spaces of contracting self-similar groups and self-similar structures. We give the condition on a contracting group such that its limit space admits a self-similar structure, and also the condition such that this self-similar structure is post-critically finite (p.c.f.). We then give necessary and sufficient conditions for a p.c.f. self-similar structure to be the limit space of a contracting self-similar group. When these conditions hold we give a construction of the contracting group. Finally, we illustrate our results with several examples.
- Subjects
GROUP theory; TOPOLOGICAL spaces; FRACTALS; SELF-similar processes; GEOMETRIC group theory; RECURSIVE functions
- Publication
International Journal of Algebra & Computation, 2012, Vol 22, Issue 7, p-1
- ISSN
0218-1967
- Publication type
Article
- DOI
10.1142/S0218196712500567