We show that, for contracting and regular self-similar graph actions, the shift maps on limit spaces are positively expansive local homeomorphisms. From this, we find that limit solenoids of contracting and regular self-similar graph actions are Smale spaces and that the unstable Ruelle algebras of the limit solenoids are strongly Morita equivalent to the Cuntz-Pimsner algebras by Exel and Pardo if self-similar graph actions satisfy the contracting, regular, pseudo free and $G$-transitive conditions.
"Smale spaces from self-similar graph actions." Rocky Mountain J. Math. 48 (4) 1359 - 1384, 2018. https://doi.org/10.1216/RMJ-2018-48-4-1359