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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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