2020/10/23 by Dworzanski, Leonid W.
#05C22 #05C90 #81Q35 #Discrete Mathematics (cs.DM) #Dynamical Systems (math.DS) #F.1.1 #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #G.2 #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2010.12528
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 ε-nets and, also, it is shown that dynamical systems of points on linear graphs have the slowest growth of the number of dynamic points