Towards Dynamic-Point Systems on Metric Graphs with Longest Stabilization Time
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A dynamical system of points on a metric graph is a discrete version of a quantum graph with localized wave packets. We study the set of dynamical systems over metric graphs that can be constructed from a given set of edges with fixed lengths. It is shown that such a set always contains a system consisting of a bead graph with vertex degrees not greater than three that demonstrates longest stabilization time. Also, it is shown that dynamical systems of points on linear graphs have the slowest growth of the number of dynamic points.
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