论文标题
部分可观测时空混沌系统的无模型预测
Directional dynamics of $\mathbb{Z}_+\times \mathbb{Z}$-actions generated by 1D-CA and the shift map
论文作者
论文摘要
在这篇简短的论文中，我们计算了$ \ Mathbb {z} _+\ times \ Mathbb {z} $的定向序列熵 - 由Cellular Automata和Shift Map生成的操作。同时，我们研究该系统的方向动力学。作为推论，我们证明存在一个序列，因此在任何方向上，上面的某些系统具有正方向序列熵。此外，借助用于方向性弱混合系统的平均千古理论，我们获得了有关组合数的数字理论的结果。
In this short paper, we compute the directional sequence entropy for of $\mathbb{Z}_+\times \mathbb{Z}$-actions generated by cellular automata and the shift map. Meanwhile, we study the directional dynamics of this system. As a corollary, we prove that there exists a sequence such that for any direction, some of the systems above have positive directional sequence entropy. Moreover, with help of mean ergodic theory for directional weak mixing systems, we obtain a result of number theory about combinatorial numbers.
