论文标题
朝着最长稳定时间的公制图上的动态点系统迈向动态点系统
Towards Dynamic-Point Systems on Metric Graphs with Longest Stabilization Time
论文作者
论文摘要
沿图边缘移动的点的动力系统可以将其视为几何离散动力系统，也可以视为带有局部波数据包的量子图的离散版本。我们通过固定长度的一组可相称的边缘来研究这些系统的集合，这些设备可以由给定的可相称的边缘构造。结果表明，始终存在一个系统，该系统由珠图组成，其顶点度不超过三个，该系统证明了这种集合中最长的稳定时间。结果将结果扩展到具有不可保密边缘的图形，使用$ \ varepsilon $ -NET的概念，并且还显示，线性图上的动力学点的动态系统的动态点数量最慢。
A dynamical system of points moving along the edges of a graph could be considered as a geometrical discrete dynamical system or as a discrete version of a quantum graph with localized wave packets. We study the set of such systems over metric graphs that can be constructed from a given set of commensurable edges with fixed lengths. It is shown that there always exists a system consisting of a bead graph with vertex degrees not greater than three that demonstrates the longest stabilization time in such a set. The results are extended to graphs with incommensurable edges using the notion of $\varepsilon$-nets and, also, it is shown that dynamical systems of points on linear graphs have the slowest growth of the number of dynamic points
