群上SFTs动力学性质的一个Rice定理

IF 0.5 4区数学 Q3 MATHEMATICS

Archiv der Mathematik Pub Date : 2025-04-29 DOI:10.1007/s00013-025-02125-x

Nicanor Carrasco-Vargas

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引用次数: 0

摘要

设G为具有不可确定多米诺骨牌问题的群，如\({\mathbb {Z}}^2\)。我们证明了g -子位移的所有非平凡动力学性质都是不可判定的，这对于G-SFTs是不成立的，并且证明了G-SFTs动力学性质的不可判定结果类似于Adian-Rabin定理。进一步证明了由不相交并和积构成单调的g - sft的每一个可计算实值动态不变量都是常数。

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On a Rice theorem for dynamical properties of SFTs on groups

Let G be a group with undecidable domino problem, such as \({\mathbb {Z}}^2\). We prove that all nontrivial dynamical properties for sofic G-subshifts are undecidable, that this is not true for G-SFTs, and an undecidability result for dynamical properties of G-SFTs similar to the Adian–Rabin theorem. Furthermore, we prove that every computable real-valued dynamical invariant for G-SFTs that is monotone by disjoint unions and products is constant.

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来源期刊

Archiv der Mathematik 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

117

审稿时长

4-8 weeks

期刊介绍： Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.