To a substitution system we assign a new matrix cocycle, defined over a natural skew-product extension of our system. The top Lyapunov exponent of the cocycle provides a lower bound for the Hoelder exponent of the spectral measure of the system. Similar results are obtained for dynamical systems corresponding to stationary sequences of substitutions, in particular, for generic translation flows.

中文翻译：

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替代系统和转换流的谱环

我们为替代系统分配了一个新的矩阵共环，定义在我们系统的自然斜积扩展上。共环的顶部李雅普诺夫指数为系统的光谱测量的 Hoelder 指数提供了下限。对于对应于固定替换序列的动态系统，特别是对于通用翻译流，获得了类似的结果。