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Open AccessArticle

Conjugacy of Dynamical Systems on Self-Similar Groups

Department of Mathematics Education, Ewha Womans University, Seoul 03760, Korea
Mathematics 2020, 8(2), 226; https://doi.org/10.3390/math8020226
Received: 13 January 2020 / Revised: 6 February 2020 / Accepted: 6 February 2020 / Published: 10 February 2020
(This article belongs to the Special Issue New Trends in Analysis and Geometry)
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.
Keywords: self-similar group; eventual conjugacy; limit dynamical system; limit solenoid; groupoid self-similar group; eventual conjugacy; limit dynamical system; limit solenoid; groupoid
MDPI and ACS Style

Yi, I. Conjugacy of Dynamical Systems on Self-Similar Groups. Mathematics 2020, 8, 226.

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