Abstract
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 language | English |
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Article number | 226 |
Journal | Mathematics |
Volume | 8 |
Issue number | 2 |
DOIs | |
State | Published - 1 Feb 2020 |
Bibliographical note
Funding Information:This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2018R1D1A1B07048313).
Funding Information:
Funding: This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2018R1D1A1B07048313).
Publisher Copyright:
© 2020 by the author.
Keywords
- Eventual conjugacy
- Groupoid
- Limit dynamical system
- Limit solenoid
- Self-similar group