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On the packing measure of the Sierpinski gasket

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LLorente Comí, Marta and Mera Rivas, Maria Eugenia and Morán Cabré, Manuel (2018) On the packing measure of the Sierpinski gasket. Nonlinearity, 31 (6). pp. 2571-2589. ISSN 0951-7715

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Official URL: https://doi.org/10.1088/1361-6544/aab31c



Abstract

We show that the s-dimensional packing measure P^{s}(S) of the Sierpinski gasket S, where s=((log3)/(log2)) is the similarity dimension of S, satisfies 1.6677≤P^{s}(S)≤1.6713.
We present a formula (see Theorem 6) that enables the achievement of the above measure bounds for this non-totally disconnected set as it shows that the symmetries of the Sierpinski gasket can be exploited to simplify the density characterization of P^{s} obtained in Morán M. (Nonlinearity, 2005) for self-similar sets satisfying the so-called Open Set Condition. Thanks to the reduction obtained in Theorem 6 we are able to handle the problem of computability of P^{s}(S) with a suitable algorithm.


Item Type:Article
Uncontrolled Keywords:Sierpinski gasket; Packing measure; Computability of fractal measures; Algorithm; Self-similar sets.
Subjects:Sciences > Mathematics
ID Code:58898
Deposited On:17 Feb 2020 12:52
Last Modified:17 Feb 2020 12:52

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