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.
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- Limit dynamical system
- Limit solenoid
- Positively expansive map
- Self-similar graph action
- Smale space