Conjugacy of dynamical systems on self-similar groups

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We show that the limits for dynamical systems of self-similar groups are eventually conjugate if, and only if, there is an isomorphism between their Deaconu groupoid preserving cocycles. For limit solenoids of self-similar groups, we show that the conjugacy of limit solenoids is equivalent to existence of isomorphism between the Deaconu groupoids of limit solenoid preserving cocycles.

Original languageEnglish
Article number226
Issue number2
StatePublished - 1 Feb 2020

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  • Eventual conjugacy
  • Groupoid
  • Limit dynamical system
  • Limit solenoid
  • Self-similar group


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