Self-similar sets with an open set condition and great variety of overlaps
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- by Christoph Bandt and Nguyen Viet Hung PDF
- Proc. Amer. Math. Soc. 136 (2008), 3895-3903
Abstract:
For a very simple family of self-similar sets with two pieces, we prove, using a technique of Solomyak, that the intersection of the pieces can be a Cantor set with any dimension in $[0,0.2]$ as well as a finite set of any cardinality $2^m$. The main point is that the open set condition is fulfilled for all these examples.References
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Additional Information
- Christoph Bandt
- Affiliation: Institute for Mathematics and Informatics, Arndt University, 17487 Greifswald, Germany
- MR Author ID: 30465
- Email: bandt@uni-greifswald.de
- Nguyen Viet Hung
- Affiliation: Department of Mathematics, Hue University, Hue, Vietnam
- Email: nvh0@yahoo.com
- Received by editor(s): March 16, 2007
- Received by editor(s) in revised form: September 19, 2007
- Published electronically: May 22, 2008
- Communicated by: Jane M. Hawkins
- © Copyright 2008 By the authors
- Journal: Proc. Amer. Math. Soc. 136 (2008), 3895-3903
- MSC (2000): Primary 28A80; Secondary 37B10, 37F20
- DOI: https://doi.org/10.1090/S0002-9939-08-09349-0
- MathSciNet review: 2425729