态射子位移的余边界与特征值
Coboundaries and eigenvalues of morphic subshifts
AI总结：
本文定义态射子位移，提出利用余边界计算其特征值的高效算法，并给出特征值生成空间维数及弱混合的充要条件。
摘要：
我们将态射子位移定义为由另一个替换的替换子位移的像生成的子位移。换言之，它是与一个最终周期的指令序列相关联的子位移。我们提出了一种利用余边界计算态射子位移特征值的高效算法。我们证明了原始指令序列的S-adic子位移的连续特征值总是与某个余边界相关联。对于态射子位移，我们给出了由特征值生成的Q-向量空间维数的刻画。此外，如果替换是幺模的且没有余边界，我们给出了子位移弱混合的充分必要条件。
英文摘要：
We define a morphic subshift as a subshift generated by the image of a substitution subshift by another substitution. In other words, it is the subshift associated with a ultimately periodic directive sequence. We present an efficient algorithm for computing eigenvalues of morphic subshifts using coboundaries. We show that continuous eigenvalues of S-adic subshifts for primitive directive sequences are always associated with some coboundary. For morphic subshifts, we provide a characterization of the dimension of the Q-vector space generated by eigenvalues. Additionally, if the substitutions are unimodular and without coboundaries, we give a necessary and sufficient condition for weak mixing of the subshift.
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