Fractal Dimension for IFS-Attractors Revisited
Journal
Qualitative Theory of Dynamical Systems
Volumen
17
Número
3
Páginas
709-722
BIBTeX
@article{quali18, author = "Fern{\'a}ndez Mart{\'i}nez, Manuel and J. L. G. Guirao", 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.", doi = "10.1007/s12346-018-0272-5", issn = "1575-5460", journal = "Qualitative Theory of Dynamical Systems", month = "October", number = "3", pages = "709-722", title = "{F}ractal {D}imension for {IFS}-{A}ttractors {R}evisited", url = "https://link.springer.com/article/10.1007/s12346-018-0272-5", volume = "17", year = "2018", } 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.