替代铺层的光谱循环

IF 0.8 3区数学 Q2 MATHEMATICS

Ergodic Theory and Dynamical Systems Pub Date : 2023-09-18 DOI:10.1017/etds.2023.64

BORIS SOLOMYAK, RODRIGO TREVIÑO

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引用次数: 1

摘要

基于一维取代流的谱环的构造[a]。布费托夫和索洛米亚克。替换系统和平移流的谱循环。j .肛门。Math. 141(1)(2020)， 165-205]被扩展到${\mathbb R}^d$中的伪自相似平铺设置，允许扩展旋转的相似性。利用该循环的点向上Lyapunov指数来限定变形瓷砖的光谱测度的局部维数。根据Treviño[随机替换铺层的定量弱混合]的工作，考虑了变形。以色列J.数学在更简单的，非随机的环境中出现。我们在这个特殊情况下回顾Treviño的一些结果，并用具体的例子说明它们。

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Spectral cocycle for substitution tilings

Abstract The construction of a spectral cocycle from the case of one-dimensional substitution flows [A. I. Bufetov and B. Solomyak. A spectral cocycle for substitution systems and translation flows. J. Anal. Math. 141 (1) (2020), 165–205] 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 the work of Treviño [Quantitative weak mixing for random substitution tilings. Israel J. Math. , to appear], in the simpler, non-random setting. We review some of the results of Treviño in this special case and illustrate them on concrete examples.

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来源期刊

Ergodic Theory and Dynamical Systems 数学-数学

CiteScore

1.70

自引率

11.10%

发文量

113

审稿时长

6-12 weeks

期刊介绍： Ergodic Theory and Dynamical Systems focuses on a rich variety of research areas which, although diverse, employ as common themes global dynamical methods. The journal provides a focus for this important and flourishing area of mathematics and brings together many major contributions in the field. The journal acts as a forum for central problems of dynamical systems and of interactions of dynamical systems with areas such as differential geometry, number theory, operator algebras, celestial and statistical mechanics, and biology.