Dynamical Systems, Linear Programming and the Monge-Kantorovich Problem
summary
Connects the Monge-Kantorovich mass‑transport problem to linear programming and dynamics by proving M = K = D in a finite adjoint‑orbit setting and extending to the semigroup of measure‑preserving maps on the annulus. Uses the Schur‑Horn polytope, doubly stochastic matrices and the momentum map; implements gradient/ispectral dynamics via the double bracket flow (an isospectral flow) and shows N! equilibria with exactly one stable equilibrium. Also outlines an infinite‑dimensional analogue linked to Toda‑type integrable systems.
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