Lastly, disjoint unions of these q i-quasiperiodic subshifts, where the qi’s are non-empty finite words over 𝒜, were looked into. By identifying all periodic points in X q, a necessary and sufficient condition for the q-quasiperiodic subshift X q to be mixing was established. It was also shown that the q-quasiperiodic subshift X q, which is the set of all q-quasiperiodic biinfinite words, is a (2| q| – 2)-memory shift of finite type. The relation between biinfinite quasiperiodicity and other notions of symmetry of words were explored. We show that, unlike in the case of right infinite words, biinfinite multi-scale quasiperiodicity does not imply uniform recurrence.
ISSN 1088-6826 (online) ISSN 0002-9939 (print) The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85. A quasiperiodic word with an infinite number of quasiperiods is called multi-scale quasiperiodic. Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics. In this case, q is said to be a quasiperiod of w. A word w over 𝒜 is said to be quasiperiodic if it has a finite proper subword q such that every position of w falls under some occurrence of q.
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