论文标题
在鲍姆斯拉格 - solarag群体上的有限类型的薄弱和强烈的基础缩影
Weakly and Strongly Aperiodic Subshifts of Finite Type on Baumslag-Solitar Groups
论文作者
论文摘要
我们研究了Baumslag-solitar群体上有限类型（SFT）的子迁移的周期性。我们表明，对于残留有限的Baumslag-solitar群体，存在强烈和弱但却不巧妙的大型SFT。特别是，这表明与$ \ mathbb {z}^2 $不同，但是像$ \ mathbb {z}^3 $一样，强度和弱的aperiodic sfts在残留有限的BS组中是不同类别的SFT。更准确地说，我们证明，由于Aubrun和Kari，BS（M，N）上的弱上性sft弱，实际上在BS上是强烈的Aperiodic（1，n）。在任何其他BS（M，N）上，弱但不强烈的上毒。此外，我们表现出一个弱但不强烈的BS（1，n）的SFT；我们表明，在BS（n，n）上存在强烈的基础SFT。
We study the periodicity of subshifts of finite type (SFT) on Baumslag-Solitar groups. We show that for residually finite Baumslag-Solitar groups there exist both strongly and weakly-but-not-strongly aperiodic SFTs. In particular, this shows that unlike $\mathbb{Z}^2$, but like $\mathbb{Z}^3$, strong and weak aperiodic SFTs are different classes of SFTs in residually finite BS groups. More precisely, we prove that a weakly aperiodic SFT on BS(m,n) due to Aubrun and Kari is, in fact, strongly aperiodic on BS(1,n); and weakly but not strongly aperiodic on any other BS(m,n). In addition, we exhibit an SFT which is weakly but not strongly aperiodic on BS(1,n); and we show that there exists a strongly aperiodic SFT on BS(n,n).
