Smale spaces from self-similar graph actions

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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.

Original languageEnglish
Pages (from-to)1359-1384
Number of pages26
JournalRocky Mountain Journal of Mathematics
Issue number4
StatePublished - 2018

Bibliographical note

Publisher Copyright:
Copyright © 2018 Rocky Mountain Mathematics Consortium.


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


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