Calculating hausdorff dimension in higher dimensional spaces
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Knowledge AreaMatemática Aplicada
SponsorsThis research received no external funding.
Realizado en/conUniversidad Politécnica de Cartagena; Universidad de Almería
Bibliographic CitationFernández-Martínez M, García Guirao JL, Sánchez-Granero MÁ. Calculating Hausdorff Dimension in Higher Dimensional Spaces. Symmetry. 2019; 11(4):564. https://doi.org/10.3390/sym11040564
In this paper, we prove the identity Hausdorff dimension, FRdand :[0,1][0,1]din a more general setting. Thus, Hausdorff dimension of higher dimensional subsets can be calculated from Hausdorff dimension of 1-dimensional subsets of [0,1]. As a consequence, Hausdorff dimension becomes available to deal with the effective calculation of the fractal dimension in applications by applying a procedure contributed by the authors in previous works. It is also worth pointing out that our results generalize both Skubalska-Rafajowicz and Garcia-Mora-Redtwitz theorems.
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