It is shown that, for nested fractals [T.Lindstrom, Mem. Amer. Math. Soc. 420, 1990], the main structural data, such as the Hausdorff dimension and measure, the geodesic distance (when it exists) induced by the immersion in Rn, and the self-similar energy can all be recovered by the description of the fractals in terms of the spectral triples considered in [D.Guido, T.Isola, in "Advances in Operator Algebras and Mathematical Physics", Theta Series in Advanced Mathematics, Bucharest 2005].
Guido, D., Isola, T. (2017). Spectral triples for nested fractals. JOURNAL OF NONCOMMUTATIVE GEOMETRY, 11(4), 1413-1436 [10.4171/JNCG/11-4-7].
Spectral triples for nested fractals
Guido, Daniele
Membro del Collaboration Group
;Isola, Tommaso
2017-01-01
Abstract
It is shown that, for nested fractals [T.Lindstrom, Mem. Amer. Math. Soc. 420, 1990], the main structural data, such as the Hausdorff dimension and measure, the geodesic distance (when it exists) induced by the immersion in Rn, and the self-similar energy can all be recovered by the description of the fractals in terms of the spectral triples considered in [D.Guido, T.Isola, in "Advances in Operator Algebras and Mathematical Physics", Theta Series in Advanced Mathematics, Bucharest 2005].File in questo prodotto:
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