多维符号动力学的普适性
Universality in Multidimensional Symbolic Dynamics
摘要：
我们证明了在有效$Z$动力系统范畴中存在一个普适系统，即一个因子作用于所有其他有效系统的普适系统。特别地，对于d $\geq 3$，存在有限型的d维移位，其对于SFT的1维子作用是普适的。另一方面，我们表明，有没有普遍有效的$Z^d$ -系统$d>1$，特别是SFT不能是普遍的秩$d>1$的子动作。因此，熵和梅德韦杰夫度和周期性数据的减少不足以使因子图存在于SFT之间。我们还讨论了动力学的细胞自动机的极限集，并表明（除了不可避免的存在一个周期点），他们可以模拟一个大类的物理系统。
英文摘要：
We show that in the category of effective $Z$ dynamical systems there is a universal system, i.e. one that factors onto every other effective system. In particular, for d $\geq 3$ there exist d-dimensional shifts of finite type which are universal for 1-dimensional subactions of SFTs. On the other hand, we show that there is no universal effective $Z^d$-system for $d>1$, and in particular SFTs cannot be universal for subactions of rank $d>1$. As a consequence, a decrease in entropy and Medvedev degree and periodic data are not sufficient for a factor map to exists between SFTs. We also discuss dynamics of cellular automata on their limit sets and show that (except for the unavoidable presence of a periodic point) they can model a large class of physical systems.
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