JournalsjncgVol. 6, No. 4pp. 801–817

Spectral triples and Gibbs measures for expanding maps on Cantor sets

  • Richard Sharp

    University of Manchester, UK
Spectral triples and Gibbs measures for expanding maps on Cantor sets  cover
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Abstract

Let T ⁣:ΛΛT \colon \Lambda \to \Lambda be an expanding map on a Cantor set. For each suitably normalized Hölder continuous potential, we construct a spectral triple from which one may recover the associated Gibbs measure as a noncommutative measure.

Cite this article

Richard Sharp, Spectral triples and Gibbs measures for expanding maps on Cantor sets . J. Noncommut. Geom. 6 (2012), no. 4, pp. 801–817

DOI 10.4171/JNCG/106