![]() A sufficient condition for such a union be a shift of finite type was given. Lastly, disjoint unions of these q i-quasiperiodic subshifts, where the qi’s are non-empty finite words over □, 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. A quasiperiodic word with an infinite number of quasiperiods is called multi-scale quasiperiodic. ![]() In this case, q is said to be a quasiperiod of w. Several classical problems in symbolic dynamics concern the characterization of the simplex of measures of maximal entropy. One is unital and the other not necessarily. van Wyk We introduce two algebras associated with a subshift over an arbitrary alphabet. This is the case in the Ledrappier subshift (the 3-dot system) and, more generally, in all two-dimensional algebraic subshifts over F p defined by a polynomial without line polynomial factors in more than one direction. A word w over □ 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. Algebras of one-sided subshifts over arbitrary alphabets Giuliano Boava, Gilles G. We study Nivats conjecture on algebraic subshifts and prove that in some of them every low complexity configuration is periodic.
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