Monotone Dynamical Systems with Polyhedral Order Cones and Dense Periodic Points

Abstract

Let X be a subset of R^n whose interior is connected and dense in X, ordered by a polyhedral cone in R^n with nonempty interior. Let T be a monotone homeomorphism of X whose periodic points are dense. Then T is periodic.

Presented at AIDS Conference on Dynamical Systems and Differential Equations, July 2016