The ϕ-Topological Conformal Dimension for the Sierpinski Carpet. Issue 1 (2nd January 2022)

• Record Type: Journal Article
• Authors: Mabrouk, Anouar Ben; Douzi, Zied; Selmi, Bilel
• Is Part Of: Journal of dynamical systems and geometric theories. Volume 20:Issue 1(2022)
• Page Start: 33
• Page End: 53
• Publication Date: 2022-01-02
• Subjects: 28A20 -- 28A75 -- 28A78 -- 28A80 -- 49Q15; Hausdorff dimension -- Topological Hausdorff dimension -- Billingsley dimension -- Sierpinski carpet -- Conformal dimension; Differentiable dynamical systems -- Periodicals; Geometry -- Periodicals; Differentiable dynamical systems; Geometry; Periodicals; 515.39
• DOI: 10.1080/1726037X.2022.2079264
• Languages: English
• ISSNs: 1726-037X

Abstract

Abstract: 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 .