Abstract:We study the dynamical properties of irregular model sets and show that the translation action on their hull always admits an infinite independence set. The dynamics can therefore not be tame and the topological sequence entropy is strictly positive. Extending the proof to a more general setting, we further obtain that tame implies regular for almost automorphic group actions on compact spaces. In the converse direction, we show that even in the restrictive case of Euclidean cut and project schemes irregular model sets may be uniquely ergodic and have zero topological entropy. This provides negative answers to questions by Schlottmann and Moody in the Euclidean setting.

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中文翻译：

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不规则的模型集和驯服动力学

摘要：我们研究了不规则模型集的动力学性质，并表明在其船体上的平移动作始终允许一个无限的独立集。因此，动力学不能驯服，并且拓扑序列熵严格为正。将证明扩展到更一般的设置，我们进一步获得了温和意味着紧致空间上几乎自守的群动作的规律性。在相反的方向上，我们表明，即使在欧几里得割和投影方案的限制性情况下，不规则模型集也可能是唯一遍历遍历的，并且拓扑熵为零。这为Schlottmann和Moody在欧几里得语环境中的问题提供了否定的答案。

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