  We investigate the iterative behaviour of continuous order preserving
subhomogeneous maps that map a polyhedral cone into itself. For these maps we
show that every bounded orbit converges to a periodic orbit and, moreover, that
there exists an a priori upper bound for the periods of periodic points that
only depends on the number of facets of the polyhedral cone. By constructing
examples on the standard positive cone, we show that the upper bound is
asymptotically sharp.
  These results are an extension of recent work by Lemmens and Scheutzow
concerning periodic orbits in the interior of the standard positive cone.
