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Monotone Dynamical Systems with Polyhedral Order Cones and Dense Periodic Points


Let X ⊂ Rn be a set whose interior is connected and dense in X, ordered by a closed convex cone K ⊂ Rn having nonempty interior. Let T: X ≈ X be an order-preserving homeomorphism. The following result is proved: Assume the set of periodic points of T is dense in X, and K is a polyhedron. Then T is periodic.

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