论文标题
部分可观测时空混沌系统的无模型预测
Multiband linear cellular automata and endomorphisms of algebraic vector groups
论文作者
论文摘要
我们提出了在物理现象的描述中广泛使用的某些多频道线性细胞自动机之间的对应关系，而在有限场上广泛使用了某些代数单位组的内态性。该对应关系基于用于任何有限场的普通发电机的通用元素的构建。我们使用这种对应关系来推断有关此类自动机的时间动力学的新结果，使用我们先前的纯代数研究矢量组的内态环的研究。这些生产“免费”是$ n $ with的固定点数量的公式，以$ n $的$ p $ addic估值，Artin-Mazur Dynamilical Dynalial Zeta功能的二分法以及用于周期轨道数量的渐近公式。由于多频线线性蜂窝自动机模拟高阶线性自动机（其中依赖于有限的许多先前的时间状态，而不仅仅是直接的前任状态），因此结果同样适用于该类别。
We propose a correspondence between certain multiband linear cellular automata - models of computation widely used in the description of physical phenomena - and endomorphisms of certain algebraic unipotent groups over finite fields. The correspondence is based on the construction of a universal element specialising to a normal generator for any finite field. We use this correspondence to deduce new results concerning the temporal dynamics of such automata, using our prior, purely algebraic, study of the endomorphism ring of vector groups. These produce 'for free' a formula for the number of fixed points of the $n$-iterate in terms of the $p$-adic valuation of $n$, a dichotomy for the Artin-Mazur dynamical zeta function, and an asymptotic formula for the number of periodic orbits. Since multiband linear cellular automata simulate higher order linear automata (in which states depend on finitely many prior temporal states, not just the direct predecessor), the results apply equally well to that class.
