论文标题
$ \ mathbb {n}^d $上的2个密码整数系统的边界复杂性和表面熵
Boundary complexity and surface entropy of 2-multiplicative integer systems on $\mathbb{N}^d$
论文作者
论文摘要
在本文中，我们介绍了边界复杂性的概念，并证明了$ \ Mathbb {n} $（或$ \ x^{\ bf p} $ x^{\ bf p} $ x^{\ bf p}_Ω \ log r] $可以实现为具有特定速度的2-MI的边界复杂性，其中R代表字母数。结果是新的，与$ \ mathbb {n}^d $ subshifts for $ d \ geq 1 $ shifts完全不同。此外，还提供了$ \ mathbb {n}^d $ 2-mis的表面熵的严格公式。这提供了一种有效的方法来计算$ \ mathbb {n}^d $ 2-mis的拓扑熵，并且还提供了$ \ mathbb {n}^d $ $ $ k $ -mis和sfts $ d \ geq 1 $和$ k \ geq 2 $之间的内在差异。
In this article, we introduce the concept of the boundary complexity and prove that for a 2-multiplicative integer system (2-MIS) $X^{p}_Ω$ on $\mathbb{N}$ (or $X^{\bf p}_Ω$ on $\mathbb{N}^d,d\geq 2$), every point in $[h(X^p_Ω), \log r]$ can be realized as a boundary complexity of a 2-MIS with a specific speed, where r stands for the number of the alphabets. The result is new and quite different from $\mathbb{N}^d$ subshifts of finite type (SFT) for $d\geq 1$. Furthermore, the rigorous formula of surface entropy for a $\mathbb{N}^d$ 2-MIS is also presented. This provides an efficient method to calculate the topological entropy for $\mathbb{N}^d$ 2-MIS and also provides an intrinsic differences between $\mathbb{N}^d$ $k$-MIS and SFTs for $d\geq 1$ and $k\geq 2$.
