论文标题
用于取代瓷砖的光谱旋转
Spectral cocycle for substitution tilings
论文作者
论文摘要
Bufetov-Solomyak [Arxiv：1802.04783]从一维取代的情况下构建光谱共生的构造，扩展到设置为伪自我的模仿瓷砖，以$ {\ mathbb r}^d $的形式设置，从而可以扩大与轮换相似的相似之处。该合子的尖端上的Lyapunov指数用于结合变形砖的光谱测量的局部维度。在treviño[arxiv：2006.16980]之后，考虑了变形，以简单的非随机设置。在此特殊情况下，我们回顾了[Arxiv：2006.16980]的定量弱混合的一些结果，并在具体示例中进行了说明。
The construction of spectral cocycle from the case of 1-dimensional substitution flows by Bufetov-Solomyak [arXiv:1802.04783] is extended to the setting of pseudo-self-similar tilings in ${\mathbb R}^d$, allowing expanding similarities with rotations. The pointwise upper Lyapunov exponent of this cocycle is used to bound the local dimension of spectral measures of deformed tilings. The deformations are considered, following Treviño [arXiv:2006.16980], in the simpler, non-random setting. We review some of the results on quantitative weak mixing from [arXiv:2006.16980] in this special case and illustrate them on concrete examples.
