Fractal Dimension for IFS-Attractors Revisited

  1. Fernández-Martínez, M 1
  2. Guirao, J L G 2
  3. Vera López, Juan Antonio 1
  1. 1 University Centre of Defence at the Spanish Air Force Academy
  2. 2 Universidad Politécnica de Cartagena
    info

    Universidad Politécnica de Cartagena

    Cartagena, España

    ROR https://ror.org/02k5kx966

Journal:
Qualitative theory of dynamical systems

ISSN: 1575-5460

Year of publication: 2018

Volume: 17

Issue: 3

Pages: 709-722

Type: Article

DOI: 10.1007/S12346-018-0272-5 DIALNET GOOGLE SCHOLAR lock_openOpen access editor

More publications in: Qualitative theory of dynamical systems

Abstract

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.

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