Monotone dynamical systems with dense periodic points

Abstract

In this paper we prove a recent conjecture by M. Hirsch, which says that if $(f,\Omega )$ is a discrete time monotone dynamical system, with $f:\Omega \to \Omega$ a homeomorphism on an open connected subset of a finite dimensional vector space, and the periodic points of $f$ are dense in $\Omega$, then $f$ is periodic.

5 pages