On cut sets of attractors of iterated function systems
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- by Benoît Loridant, Jun Luo, Tarek Sellami and Jörg M. Thuswaldner PDF
- Proc. Amer. Math. Soc. 144 (2016), 4341-4356 Request permission
Abstract:
In this paper, we study cut sets of attractors of iterated function systems (IFS) in $\mathbb {R}^d$. Under natural conditions, we show that all irreducible cut sets of these attractors are perfect sets or single points. This leads to a criterion for the existence of cut points of IFS attractors. If the IFS attractors are self-affine tiles, our results become algorithmically checkable and can be used to exhibit cut points with the help of Hata graphs. This enables us to construct cut points of some self-affine tiles studied in the literature.References
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Additional Information
- Benoît Loridant
- Affiliation: Montanuniversität Leoben, Franz Josef Strasse 18, Leoben 8700, Austria
- MR Author ID: 824107
- Jun Luo
- Affiliation: Department of Statistics, Sun Yat-Sen University, Guangzhou 512075, People’s Republic of China
- MR Author ID: 643272
- Tarek Sellami
- Affiliation: Department of mathematics, Faculty of sciences of Sfax, Sfax University, Route Soukra, BP 802, 3018 Sfax, Tunisia
- MR Author ID: 912287
- Jörg M. Thuswaldner
- Affiliation: Montanuniversität Leoben, Franz Josef Strasse 18, Leoben 8700, Austria
- MR Author ID: 612976
- ORCID: 0000-0001-5308-762X
- Received by editor(s): December 4, 2014
- Received by editor(s) in revised form: December 7, 2015
- Published electronically: May 31, 2016
- Additional Notes: The first and fourth authors were supported by the project P22855 of the FWF (Austrian Science Fund), the project I 1136 of the FWF and the ANR (French National Research Agency). The second author was supported by the projects 10971233 and 11171123 of the Chinese National Natural Science Foundation.
- Communicated by: Michael Wolf
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 4341-4356
- MSC (2010): Primary 28A80, 52C20, 54D05
- DOI: https://doi.org/10.1090/proc/13182
- MathSciNet review: 3531184