It is shown that many important features of nested fractals, such as the Hausdorff dimension and measure, the geodesic distance induced by the immersion in Rn (when it exists), and the self-similar energy can be recovered by the description of the fractal in terms of spectral triples. We describe in particular the case of the Vicsek square, showing that all self-similar energies can be described through a deformation of the square to a rhombus.
Guido, D., & Isola, T. (2016). New Results on Old Spectral Triples for Fractals. In F.C. Daniel Alpay (a cura di), Noncommutative Analysis, Operator Theory and Applications (pp. 261-270). Springer International Publishing [10.1007/978-3-319-29116-1_12].
Autori: | ||
Autori: | Guido, D; Isola, T | |
Titolo: | New Results on Old Spectral Triples for Fractals | |
Data di pubblicazione: | 1-lug-2016 | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/978-3-319-29116-1_12 | |
Settore Scientifico Disciplinare: | Settore MAT/05 - Analisi Matematica | |
Lingua: | English | |
Rilevanza: | Rilevanza internazionale | |
Tipo: | Articolo scientifico in atti di convegno | |
Tipologia: | Contributo in libro | |
Citazione: | Guido, D., & Isola, T. (2016). New Results on Old Spectral Triples for Fractals. In F.C. Daniel Alpay (a cura di), Noncommutative Analysis, Operator Theory and Applications (pp. 261-270). Springer International Publishing [10.1007/978-3-319-29116-1_12]. | |
Appare nelle tipologie: | 03 - Contributo in libro |
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