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Monotone dynamical systems with polyhedral order cones and dense periodic points

Abstract

Let X ⊂ R be a set whose interior is connected and dense in X, ordered by a closed convex cone K ⊂ R 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. n n

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