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On the open set condition for self-similar fractals

Author(s): Christoph Bandt; Nguyen Viet Hung; Hui Rao
Journal: Proc. Amer. Math. Soc. 134 (2006), 1369-1374.
MSC (2000): Primary 28A80; Secondary 28A75
Posted: October 6, 2005
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Abstract: For self-similar sets, the existence of a feasible open set is a natural separation condition which expresses geometric as well as measure-theoretic properties. We give a constructive approach by defining a central open set and characterizing those points which do not belong to feasible open sets.

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K.J. Falconer, Fractal Geometry, Wiley, 1990. MR 1102677 (92j:28008)

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Additional Information:

Christoph Bandt
Affiliation: Institute for Mathematics, Arndt University, 17487 Greifswald, Germany
Email: bandt@uni-greifswald.de

Nguyen Viet Hung
Affiliation: Institute for Mathematics, Arndt University, 17487 Greifswald, Germany
Email: nvh0@yahoo.com

Hui Rao
Affiliation: Department of Mathematics, Tsinghua University, P.O. Box 100084, Beijing, People's Republic of China
Email: HRao@math.tsinghua.edu.cn

DOI: 10.1090/S0002-9939-05-08300-0
PII: S 0002-9939(05)08300-0
Keywords: Self-similar, fractals, iterated function system
Received by editor(s): October 26, 2004,
Received by editor(s) in revised form: December 2, 2004
Posted: October 6, 2005
Additional Notes: The third author was supported by the German Research Foundation (DFG), and the second author was supported by the Vietnamese Government and the German Academic Exchange Service (DAAD)
Communicated by: David Preiss
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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