 Irreducible fractal structures for Moran type theoremsM.A. Sánchez-Granero and M. Fernández-Martínez Chaos, Solitons & Fractals, 2019, vol. 119, issue C, 29-36 Abstract: In this paper, we introduce a separation property for self-similar sets which is necessary to reach the equality between the similarity dimension and the Hausdorff dimension of these spaces. The similarity boundary of a self-similar set is investigated from the viewpoint of that property. In this way, the strong open set condition (in the self-similar set setting) posed by Keesling and Krishnamurthi has been weakened leading to a Moran type theorem. Moreover, both a result based on a conjecture posed by Deng and Lau as well as an improved version of a theorem due to Bandt and Rao have been contributed regarding the size of the overlaps among the pieces of a self-similar set. Several (equivalent) conditions leading to the equality between the similarity dimension and a new Hausdorff type dimension for attractors described in terms of finite coverings are also provided. Finally, we list some open questions. Keywords: Open set condition; Iterated function system; Weak separation property; Moran’s theorem; Self-similar set; Hausdorff dimension (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:119:y:2019:i:c:p:29-36 DOI: 10.1016/j.chaos.2018.12.009 Access Statistics for this article Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros More articles in Chaos, Solitons & Fractals from Elsevier |
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