Conjugacy of dynamical systems on self-similar groups

Inhyeop Yi

doi:10.3390/math8020226

Conjugacy of dynamical systems on self-similar groups

Inhyeop Yi

Department of Mathematics Education

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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
Article number	226
Journal	Mathematics
Volume	8
Issue number	2
DOIs	https://doi.org/10.3390/math8020226
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

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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.",

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AB - 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.

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ER -

Conjugacy of dynamical systems on self-similar groups

Abstract

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Keywords

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