Monotone dynamical systems with polyhedral order cones and dense periodic points
- Author(s): Hirsch, MW
- et al.
Published Web Locationhttps://doi.org/10.3934/Math.2017.1.24
© 2016, M. W. Hirsch, licensee AIMS Press. 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.