Fractal Dimension for IFS-Attractors Revisited

Fernández-Martínez, M ^[2] ; Guirao, J L G ^[1] ; Vera López, Juan Antonio ^[2]
1. [1] Universidad Politécnica de Cartagena
  
  Universidad Politécnica de Cartagena
  
  Cartagena, España
2. [2] University Centre of Defence at the Spanish Air Force Academy
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 17, Nº 3, 2018, págs. 709-722
Idioma: inglés
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Resumen
- One of the milestones in Fractal Geometry is the so-called Moran’s Theorem, which allows the calculation of the similarity dimension of any strict self-similar set under the open set condition. In this paper, we contribute a generalized version of the Moran’s theorem, which does not require the OSC to be satisfied by the similitudes that give rise to the corresponding attractor. To deal with, two generalized versions for the classical fractal dimensions, namely, the box and the Hausdorff dimensions, are explored in terms of fractal structures, a kind of uniform spaces.