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Monotone Dynamical Systems with Polyhedral Order Cones and Dense Periodic Points

Department of Mathematics, University of Wisconsin, Madison WI 53706, USA

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Let $X\subset \mathbb{R}^{n}$ be a set whose interior is connected and dense in $X$, ordered by a closed convex cone $K\subset \mathbb{R}^{n}$ having nonempty interior. Let $T: X\approx X$ 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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References

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