Almost specification and renewality in spacing shifts
Authors
Abstract:
Let $(Sigma_P,sigma_P)$ be the space of a spacing shifts where $Psubset mathbb{N}_0=mathbb{N}cup{0}$ and $Sigma_P={sin{0,1}^{mathbb{N}_0}: s_i=s_j=1 mbox{ if } |i-j|in P cup{0}}$ and $sigma_P$ the shift map. We will show that $Sigma_P$ is mixing if and only if it has almost specification property with at least two periodic points. Moreover, we show that if $h(sigma_P)=0$, then $Sigma_P$ is almost specified and if $h(sigma_P)>0$ and $Sigma_P$ is almost specified, then it is weak mixing. Also, some sufficient conditions for a coded $Sigma_P$ being renewal or uniquely decipherable is given. At last we will show that here are only two conjugacies from a transitive $Sigma_P$ to a subshift of ${0,1}^{mathbb{N}_0}$.
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Journal title
volume 43 issue 3
pages 885- 896
publication date 2017-06-30
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