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
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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.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