Work

From Self-Similar Structures to Self-Similar Groups

Year: 2010

Type: preprint

Abstract: We explore the relationship between 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 p.c.f. We then give the necessary and sufficient condition on a p.c.f. self-similar structure such that there exists a contracting group whose limit space has an isomorphic self-similar structure; in this case, we provide a construction that produces such a contracting group. Finally, we illustrate our results with several examples.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1011.1817

Authors: Kelleher, Daniel J., Steinhurst, Benjamin A., Wong, Chuen-Ming M.

Institutions: University of Connecticut, Cornell University, Princeton University, Columbia University

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Award: Random, Stochastic, and Self-similar Equations

OpenAlex ID: W2951336805

Cites: 4

Cited by:

Related to: 13