Subshifts with sparse traces

On the Trace Subshifts of Fractional Multiplication Automata

We address the dynamics of the cellular automaton (CA) that multiplies by $p/q$ in base $pq$ (for coprime $p>q>1$) by studying its trace subshift. We present a conjugacy of the trace to a previously studied base-$p/q$ numeration system. We also show that the trace subshift is not synchronizing and in particular not sofic. As a byproduct we compute its complexity function and we conclude by presenting an example of a sofic shift with the same complexity function.

极小零熵子移位可沿任意稀疏集无限制

Minimal zero entropy subshifts can be unrestricted along any sparse set

该研究简化证明了零Banach密度稀疏集上极小零熵子移位可呈现任意行为，给出更通用的多项式Sarnak猜想反例，说明仅极小性和零熵假设无法推出相关结论。

Sofic Trace of a Cellular Automaton

The trace subshift of a cellular automaton is the subshift of all possible columns that may appear in a space-time diagram, ie the infinite sequence of states of a particular cell of a configuration; in the language of symbolic dynamics one says that it is a factor system. In this paper we study conditions for a sofic subshift to be the trace of a cellular automaton.

三维稀疏列SFT

A Three-Dimensional SFT with Sparse Columns

本文构建了一个非平凡的三维有限型子移位，其投影Z-子动力学为2稀疏，即任一垂直列中最多有两个非零符号。该子移位在子动力学方向上是确定性的，因此与部分单元自动机的时间空间图集拓扑共轭。还提出了由Wang立方体定义的变体及二元字母表的子移位。