English

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 RnR^n, 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

R2 v1 2026-06-22T12:39:38.083Z