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Proceedings of the American Mathematical Society

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On Hausdorff dimension of recurrent net fractals


Author: Sergio Stella
Journal: Proc. Amer. Math. Soc. 116 (1992), 389-400
MSC: Primary 58F12; Secondary 28A78
DOI: https://doi.org/10.1090/S0002-9939-1992-1094507-X
Corrigendum: Proc. Amer. Math. Soc. 121 (1994), 1309-1311.
MathSciNet review: 1094507
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Abstract: We estimate the Hausdorff dimension of recurrent net fractals showing that it coincides with the box-counting dimension. This is done for geometric constructions in a complete metric space, generalizing well-known theorems about self-similar sets. In particular, it follows that what is really essential in the dimension estimates of self-similar sets are their metric features and not the dynamical ones.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1094507-X
Keywords: Dimension, fractal, self-similar set, recurrent net fractal
Article copyright: © Copyright 1992 American Mathematical Society

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