Aperiodic points in -subshifts
arXiv preprint arXiv:1805.08829, 2018•arxiv.org
We consider the structure of aperiodic points in $\mathbb Z^ 2$-subshifts, and in particular
the positions at which they fail to be periodic. We prove that if a $\mathbb Z^ 2$-subshift
contains points whose smallest period is arbitrarily large, then it contains an aperiodic point.
This lets us characterise the computational difficulty of deciding if an $\mathbb Z^ 2$-subshift
of finite type contains an aperiodic point. Another consequence is that $\mathbb Z^ 2$-
subshifts with no aperiodic point have a very strong dynamical structure and are almost …
the positions at which they fail to be periodic. We prove that if a $\mathbb Z^ 2$-subshift
contains points whose smallest period is arbitrarily large, then it contains an aperiodic point.
This lets us characterise the computational difficulty of deciding if an $\mathbb Z^ 2$-subshift
of finite type contains an aperiodic point. Another consequence is that $\mathbb Z^ 2$-
subshifts with no aperiodic point have a very strong dynamical structure and are almost …
We consider the structure of aperiodic points in -subshifts, and in particular the positions at which they fail to be periodic. We prove that if a -subshift contains points whose smallest period is arbitrarily large, then it contains an aperiodic point. This lets us characterise the computational difficulty of deciding if an -subshift of finite type contains an aperiodic point. Another consequence is that -subshifts with no aperiodic point have a very strong dynamical structure and are almost topologically conjugate to some -subshift. Finally, we use this result to characterize sets of possible slopes of periodicity for -subshifts of finite type.
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