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Characteristic measures of symbolic dynamical systems

Part of: Topological dynamics

Published online by Cambridge University Press:  18 March 2021

JOSHUA FRISCH  and
OMER TAMUZ Open the ORCID record for OMER TAMUZ [Opens in a new window]
JOSHUA FRISCH
Affiliation:
California Institute of Technology, Pasadena, CA, USA (e-mail: [email protected])
OMER TAMUZ*
Affiliation:
California Institute of Technology, Pasadena, CA, USA (e-mail: [email protected])
*
e-mail: [email protected]
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Abstract

A probability measure is a characteristic measure of a topological dynamical system if it is invariant to the automorphism group of the system. We show that zero entropy shifts always admit characteristic measures. We use similar techniques to show that automorphism groups of minimal zero entropy shifts are sofic.

Keywords

symbolic dynamicsautomorphism groupsgroup actions

MSC classification

Primary: 37B10: Symbolic dynamics
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 42 , Issue 5 , May 2022 , pp. 1655 - 1661
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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