When the weak separation condition implies the generalized finite type condition
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- by Kathryn E. Hare, Kevin G. Hare and Alex Rutar
- Proc. Amer. Math. Soc. 149 (2021), 1555-1568
- DOI: https://doi.org/10.1090/proc/15307
- Published electronically: February 4, 2021
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Abstract:
We prove that an iterated function system of similarities on $\mathbb {R}$ that satisfies the weak separation condition and has an interval as its self-similar set is of generalized finite type. It is unknown if the assumption that the self-similar set is an interval is necessary.References
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Bibliographic Information
- Kathryn E. Hare
- Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, N2L 3G1 Canada
- MR Author ID: 246969
- Email: kehare@uwaterloo.ca
- Kevin G. Hare
- Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, N2L 3G1 Canada
- MR Author ID: 690847
- Email: kghare@uwaterloo.ca
- Alex Rutar
- Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, N2L 3G1 Canada
- Address at time of publication: Mathematical Institute, North Haugh, St Andrews, Fife KY16 9SS, Scotland
- ORCID: 0000-0001-5173-992X
- Email: arutar@uwaterloo.ca
- Received by editor(s): March 17, 2020
- Received by editor(s) in revised form: August 5, 2020
- Published electronically: February 4, 2021
- Additional Notes: The first author was supported by NSERC Grant 2016-03719. The second author was supported by NSERC Grant 2019-03930. The third author was supported by both these grants and the University of Waterloo.
- Communicated by: Javad Mashreghi
- © Copyright 2021 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 149 (2021), 1555-1568
- MSC (2020): Primary 28A80
- DOI: https://doi.org/10.1090/proc/15307
- MathSciNet review: 4242311