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

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...

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Bibliographic Details
Published in:	Proceedings of the American Mathematical Society Vol. 136; no. 11; pp. 3895 - 3903
Main Authors:	Bandt, Christoph, Hung, Nguyen Viet
Format:	Journal Article
Language:	English
Published:	Providence, RI American Mathematical Society 01-11-2008
Subjects:	Cantor set Coefficients Combinatorics Exact sciences and technology Fractals General mathematics General, history and biography Geometric planes Hausdorff dimensions Mathematical theorems Mathematics Power series Power series coefficients Sciences and techniques of general use Intersection Cantor set Mathematics Overlap Variety Selfsimilarity
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Summary:	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.
ISSN:	0002-9939 1088-6826
DOI:	10.1090/S0002-9939-08-09349-0