  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 $f\colon
\Omega\to\Omega$ 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.
