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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Dimension functions for fractal sets associated to series
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by Manuel Morán
Proc. Amer. Math. Soc. 120 (1994), 749-754
DOI: https://doi.org/10.1090/S0002-9939-1994-1186131-7

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.
References
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Bibliographic Information
  • © Copyright 1994 American Mathematical Society
  • 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