Hausdorff Measures and KMS States

摘要

Given a compactmetric space X and a local homeomorphism T : X → X satisfying a local scaling property, we show that the Hausdorff measure on X gives rise to a KMS state on the C~?-algebra naturally associated to the pair (X, T) such that the inverse temperature coincides with the Hausdorff dimension. We prove that the KMS state is unique under some mild hypotheses. We then use our results to describe KMS states on Cuntz algebras, graph algebras, and certain C~?-algebras associated to fractafolds.