Similarity dimension for IFS-attractors

Issue title: Applied Mathematics Related to Nonlinear Problems

Guest editors: Juan L.G. Guirao and Wei Gao

Article type: Research Article

Authors: Fernández-Martínez, M.^{a; *} | Guirao, Juan L.G.^b | Vera, J.A.^a

Affiliations: [a] University Centre of Defence at the Spanish Air Force Academy, MDE-UPCT, 30720 Santiago de la Ribera, Región de Murcia, Spain | [b] Departamento de Matemática Aplicada y Estadística. Universidad Politécnica de Cartagena, Hospital de Marina, 30203 Cartagena, Región de Murcia, Spain

Correspondence: [*] Corresponding author. M. Fernández-Martínez, University Centre of Defence at the Spanish Air Force Academy, MDE-UPCT, 30720 Santiago de la Ribera, Región de Murcia, Spain. E-mail: fmm124@gmail.com.

Abstract: Moran’s Theorem is one of the milestones in Fractal Geometry. It allows the calculation of the similarity dimension of any (strict) self-similar set lying under the open set condition. Throughout a new fractal dimension we provide in the context of fractal structures, we generalize such a classical result for attractors which are required to satisfy no separation properties.

Keywords: Fractal, iterated function system, IFS-attractor, fractal structure, fractal dimension, box dimension, Hausdorff dimension

DOI: 10.3233/JIFS-169312

Journal: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 5, pp. 2631-2635, 2017