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The ϕ-Topological Conformal Dimension for the Sierpinski Carpet
Journal article   Peer reviewed

The ϕ-Topological Conformal Dimension for the Sierpinski Carpet

Anouar Ben Mabrouk, Zied Douzi and Bilel Selmi
Journal of dynamical systems and geometric theories, Vol.20(1), pp.33-53
02/01/2022
DOI: https://doi.org/10.1080/1726037X.2022.2079264

Abstract

Billingsley dimension Conformal dimension Hausdorff dimension Sierpinski carpet Topological Hausdorff dimension
In this paper, a generalized fractal dimension is introduced based on a combination of the topological dimension, conformal dimension, and the ϕ-conformal dimension. Lower and upper bound estimates of the new variant of dimension are provided for the case of the Sierpinski carpet fractal set. Moreover, the equality of such bounds is proved for a large class of the basic measure ϕ.

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