Conjugacy of Dynamical Systems on Self-Similar Groups

Inhyeop Yi
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Inhyeop Yi: Department of Mathematics Education, Ewha Womans University, Seoul 03760, Korea

Mathematics, 2020, vol. 8, issue 2, 1-12

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.

Keywords: self-similar group; eventual conjugacy; limit dynamical system; limit solenoid; groupoid (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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