Spectral triples for nested fractals
Operator Algebras
2017-12-19 v2
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 , 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].
Keywords
Cite
@article{arxiv.1601.08208,
title = {Spectral triples for nested fractals},
author = {Daniele Guido and Tommaso Isola},
journal= {arXiv preprint arXiv:1601.08208},
year = {2017}
}
Comments
19 pages, 1 figure. Some points have been clarified, the introduction has been expanded in order to better explain the purpose of the paper. This version will appear in JNCG