Spectral triples and Gibbs measures for expanding maps on Cantor sets

2010/09/29 by Sharp, Richard
#37D20 (Secondary) #37D35 #46L51 #58B34 (Primary) 37C30 #Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1009.5887

Abstract

Let T : Λ→ Λ 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.

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