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Self-similar sets with an open set condition and great variety of overlaps
Author(s):
Christoph
Bandt;
Nguyen
Viet
Hung
Journal:
Proc. Amer. Math. Soc.
136
(2008),
3895-3903.
MSC (2000):
Primary 28A80;
Secondary 37B10, 37F20
Posted:
May 22, 2008
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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]$](/proc/2008-136-11/S0002-9939-08-09349-0/gif-abstract0/img1.gif) as well as a finite set of any cardinality  . 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
Email:
bandt@uni-greifswald.de
Nguyen
Viet
Hung
Affiliation:
Department of Mathematics, Hue University, Hue, Vietnam
Email:
nvh0@yahoo.com
DOI:
10.1090/S0002-9939-08-09349-0
PII:
S 0002-9939(08)09349-0
Received by editor(s):
March 16, 2007,
Received by editor(s) in revised form:
September 19, 2007
Posted:
May 22, 2008
Communicated by:
Jane M. Hawkins
Copyright of article:
Copyright
2008,
By the authors
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