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Proceedings of the American Mathematical Society

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

 

 

Dimension functions for fractal sets associated to series


Author: Manuel Morán
Journal: Proc. Amer. Math. Soc. 120 (1994), 749-754
MSC: Primary 28A78; Secondary 28A80
DOI: https://doi.org/10.1090/S0002-9939-1994-1186131-7
MathSciNet review: 1186131
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Abstract: In this article we analyze suitable dimension functions for the measure of fractal sets associated to certain absolutely convergent series of vectors of $ {\mathbb{R}^n}$. The complex binomial series provides an example of a family of fractals, all of them with the same Hausdorff dimension but with a totally ordered family of suitable dimension functions indexed by a parameter with range in a real interval. We also show a construction, based on sets associated to series, to obtain fractal sets with given dimension function.


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DOI: https://doi.org/10.1090/S0002-9939-1994-1186131-7
Keywords: Dimension, fractal
Article copyright: © Copyright 1994 American Mathematical Society