准周期无限字：多尺度情形及动力学性质
Quasiperiodic infinite words : multi-scale case and dynamical properties
摘要：
一个无限字x称为拟周期的，如果存在一个有限字q，使得x被q的出现所覆盖（这样的q称为x的拟周期）。使用派生的概念，我们表明，这个定义是不足以暗示任何对称性的一个无限的词。因此，我们引入多尺度准周期词，即准周期词，承认无限数量的准周期。这样的词是一致递归的，这允许我们研究它们产生的子移位。证明了多尺度拟周期子移位是唯一遍历的，并且具有零拓扑熵和零Kolmogorov复杂度。Sturmian子位移被证明是多尺度准周期的。
英文摘要：
An infinite word x is said to be quasiperiodic if there exists a finite word q such that x is covered by occurrences of q (such a q is called a quasiperiod of x). Using the notion of derivation, we show that this definition is not sufficient to imply any symmetry in an infinite word. Therefore we introduce multi-scale quasiperiodic words, i.e. quasiperiodic words that admit an infinite number of quasiperiods. Such words are uniformly recurrent, this allows us to study the subshift they generate. We prove that multi-scale quasiperiodic subshifts are uniquely ergodic and have zero topological entropy as well as zero Kolmogorov complexity. Sturmian subshifts are shown to be multi-scale quasiperiodic.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
