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New Results on Old Spectral Triples for Fractals

  • Daniele GuidoEmail author
  • Tommaso Isola
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 252)

Abstract

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 \(\mathbb{R}^n\) (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.

Keywords

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

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniv. Roma Tor VergataRomaItaly

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