Fractals in Noncommutative Geometry

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dc.creatorGuido, Daniele
dc.creatorIsola, Tommaso
dc.date2001-02-27
dc.date.accessioned2026-07-07T04:40:23Z
dc.date.available2026-07-07T04:40:23Z
dc.descriptionTo any spectral triple (A,D,H) a dimension d is associated, in analogy with the Hausdorff dimension for metric spaces. Indeed d is the unique number, if any, such that |D|^-d has non trivial logarithmic Dixmier trace. Moreover, when d is finite non-zero, there always exists a singular trace which is finite nonzero on |D|^-d, giving rise to a noncommutative integration on A. Such results are applied to fractals in R, using Connes' spectral triple, and to limit fractals in R^n, a class which generalises self-similar fractals, using a new spectral triple. The noncommutative dimension or measure can be computed in some cases. They are shown to coincide with the (classical) Hausdorff dimension and measure in the case of self-similar fractals.
dc.description15 pages, LaTeX with fic-l.cls at ftp://ftp.ams.org/pub/author-info/packages/fic/amslatex/fic-l.cls To appear in the proceedings of the conference "Mathematical Physics in Mathematics and Physics", Siena 2000
dc.identifierhttps://arxiv.org/abs/math/0102209
dc.identifierhttp://arxiv.org/abs/math/0102209
dc.identifierin the Proceedings of the Conference "Mathematical Physics in Mathematics and Physics", Siena 2000, R. Longo Ed., Fields Institute Communications, Vol. 30, AMS, Providence, RI, 2001
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61011
dc.subjectOperator Algebras
dc.subject46Lxx; 28A80
dc.titleFractals in Noncommutative Geometry
dc.typetext

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