Hausdorff measures and KMS states Marius IonescuAlex Kumjian 46L4046L3037D3537B10Operator algebrasdynamical systemsKMS statesHausdorff measure Given a compact metric space $X$ and a local homeomorphism $T:X\to X$ 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 with 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 with fractafolds. Indiana University Mathematics Journal 2013 text pdf 10.1512/iumj.2013.62.4904 10.1512/iumj.2013.62.4904 en Indiana Univ. Math. J. 62 (2013) 443 - 463 state-of-the-art mathematics http://iumj.org/access/