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FROM SELF-SIMILAR STRUCTURES TO SELF-SIMILAR GROUPS

DANIEL J. KELLEHER

Department of Mathematics, University of Connecticut, Storrs, CT 06269, USA

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BENJAMIN A. STEINHURST

Department of Mathematics, Cornell University, Ithaca, NY 14853, USA

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, and

CHUEN-MING M. WONG

Department of Mathematics, Columbia University, New York, NY 10027, USA

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https://doi.org/10.1142/S0218196712500567Cited by:4 (Source: Crossref)

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.

Keywords:

AMSC: Primary 20E08, Secondary 20F65, Secondary 28A80

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