We show that the Smale spaces from self-similar groups are topologically mixing and their stable algebra and stable Ruelle algebra are strongly Morita equivalent to groupoid algebras of Anantharaman-Delaroche and Deaconu. And we show that associated to a postcritically finite hyperbolic rational function is an AT-algebra of real-rank zero with a unique trace state.
"-Algebras from Groupoids on Self-Similar Groups." Abstr. Appl. Anal. 2013 (SI57) 1 - 7, 2013. https://doi.org/10.1155/2013/579042