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Self-similar sets with an open set condition and great variety of overlaps

Authors: Christoph Bandt and Nguyen Viet Hung
Journal: Proc. Amer. Math. Soc. 136 (2008), 3895-3903
MSC (2000): Primary 28A80; Secondary 37B10, 37F20
Published electronically: May 22, 2008
MathSciNet review: 2425729
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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.

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Additional Information

Christoph Bandt
Affiliation: Institute for Mathematics and Informatics, Arndt University, 17487 Greifswald, Germany

Nguyen Viet Hung
Affiliation: Department of Mathematics, Hue University, Hue, Vietnam

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
Article copyright: © Copyright 2008 By the authors

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