投影熵与电线位移
Projectional entropy and the electrical wire shift
摘要：
本文给出了有限型$W^{\text{el}}$的一个可扩展的块胶合$\mathbb Z^3$移位，其中对于二维子格$L:=\mathbb Z \vec{e}_1+\mathbb Z\vec{e}_2\subsetneq\mathbb Z^3$，其拓扑熵等于$L$ -投影熵，但$W^{\text{el}}$不是$W^{\text{el}}_L$的完全$\mathbb Z$扩展.特别地，这个例子表明[3]的定理4.1不能推广到$r>1$的$r$维子格$L$.然而，我们能够在与[3]相同的混合假设下，重新证明和推广关于一般（非SFT）$\mathbb Z^d$移位的一维子格的结果，并且通过提出更强的混合条件，我们也得到了高维子格的相应陈述。
英文摘要：
In this paper we present an extendible, block gluing $\mathbb Z^3$ shift of finite type $W^{\text{el}}$ in which the topological entropy equals the $L$-projectional entropy for a two-dimensional sublattice $L:=\mathbb Z \vec{e}_1+\mathbb Z\vec{e}_2\subsetneq\mathbb Z^3$, even so $W^{\text{el}}$ is not a full $\mathbb Z$ extension of $W^{\text{el}}_L$. In particular this example shows that Theorem 4.1 of [3] does not generalize to $r$-dimensional sublattices $L$ for $r>1$. Nevertheless we are able to reprove and extend the result about one-dimensional sublattices for general (non-SFT) $\mathbb Z^d$ shifts under the same mixing assumption as in [3] and by posing a stronger mixing condition we also obtain the corresponding statement for higher-dimensional sublattices.
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