TY - JOUR
T1 - On the number of ergodic measures for minimal shifts with eventually constant complexity growth
AU - Damron, Michael
AU - Fickenscher, Jon
N1 - Publisher Copyright:
© 2016 Cambridge University Press.
PY - 2017/10/1
Y1 - 2017/10/1
N2 - In 1985, Boshernitzan showed that a minimal (sub)shift satisfying a linear block growth condition must have a bounded number of ergodic probability measures. Recently, this bound was shown to be sharp through examples constructed by Cyr and Kra. In this paper, we show that under the stronger assumption of eventually constant growth, an improved bound exists. To this end, we introduce special Rauzy graphs. Variants of the well-known Rauzy graphs from symbolic dynamics, these graphs provide an explicit description of how a Rauzy graph for words of length relates to the one for words of length for each .
AB - In 1985, Boshernitzan showed that a minimal (sub)shift satisfying a linear block growth condition must have a bounded number of ergodic probability measures. Recently, this bound was shown to be sharp through examples constructed by Cyr and Kra. In this paper, we show that under the stronger assumption of eventually constant growth, an improved bound exists. To this end, we introduce special Rauzy graphs. Variants of the well-known Rauzy graphs from symbolic dynamics, these graphs provide an explicit description of how a Rauzy graph for words of length relates to the one for words of length for each .
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U2 - 10.1017/etds.2015.138
DO - 10.1017/etds.2015.138
M3 - Article
AN - SCOPUS:84963704476
SN - 0143-3857
VL - 37
SP - 2099
EP - 2130
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 7
ER -