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Working paper

How the permutation of edges of a metric graph affects the number of points moving along the edges

arxiv.org. math. Cornell University, 2014. No. 1410.5015.
V.L. Chernyshev, Tolchennikov A.
We consider a dynamical system on a metric graph, that corresponds to a semiclassical solution of a time-dependent Schrodinger equation. We omit all details concerning mathematical physics and work with a purely discrete problem. We find a weak inequality representation for the number of points coming out of the vertex of an arbitrary tree graph. We apply this construction to an "H-junction" graph. We calculate the difference between numbers of moving points corresponding to the permutation of edges. Then we find a symmetrical difference of the number of points moving along the edges of a metric graph.