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Journal of Noncommutative Geometry

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Volume 11, Issue 4, 2017, pp. 1413–1436
DOI: 10.4171/JNCG/11-4-7

Published online: 2017-12-15

Spectral triples for nested fractals

Daniele Guido[1] and Tommaso Isola[2]

(1) Università di Roma Tor Vergata, Rome, Italy
(2) Università di Roma Tor Vergata, Rome, Italy

It is shown that, for nested fractals [31], the main structural data, such as the Hausdorff dimension and measure, the geodesic distance (when it exists) induced by the immersion in $\mathbb R^n$, and the self-similar energy can all be recovered by the description of the fractals in terms of the spectral triples considered in [18].

Keywords: Spectral triple, nested fractal, self-similar energy, Hausdorff dimension, noncommutative distance

Guido Daniele, Isola Tommaso: Spectral triples for nested fractals. J. Noncommut. Geom. 11 (2017), 1413-1436. doi: 10.4171/JNCG/11-4-7