تقرير
Amorphic complexity of group actions with applications to quasicrystals
| العنوان: | Amorphic complexity of group actions with applications to quasicrystals |
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| المؤلفون: | Fuhrmann, Gabriel, Gröger, Maik, Jäger, Tobias, Kwietniak, Dominik |
| المصدر: | Trans. Am. Math. Soc. 376:2395-2418 (2023) |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Dynamical Systems |
| الوصف: | In this article, we define amorphic complexity for actions of locally compact $\sigma$-compact amenable groups on compact metric spaces. Amorphic complexity, originally introduced for $\mathbb Z$-actions, is a topological invariant which measures the complexity of dynamical systems in the regime of zero entropy. We show that it is tailor-made to study strictly ergodic group actions with discrete spectrum and continuous eigenfunctions. This class of actions includes, in particular, Delone dynamical systems related to regular model sets obtained via Meyer's cut and project method. We provide sharp upper bounds on amorphic complexity of such systems. In doing so, we observe an intimate relationship between amorphic complexity and fractal geometry. Comment: 26 pages, AAM version |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1090/tran/8700 |
| URL الوصول: | http://arxiv.org/abs/2101.05034 |
| رقم الأكسشن: | edsarx.2101.05034 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1090/tran/8700 |
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