  Let $\MSpace$ be a locally compact metric space and let
$\pMap:\MSpace\to\MSpace$ be a not expansive map. We prove that for each
$\ppa_0\in\MSpace$ the sequence $\ppa_0,\pMap(\ppa_0),\pMap^2(\ppa_0),\ldots$
is either relatively compact in $\MSpace$ or compactly divergent in $\MSpace$.
As applications we study the structure of the functions which are limits of the
iterates of the map $\pMap$ and we prove the analyticity of the set of
$\pMap$-recurrent points when $\pMap:\MSpace\to\MSpace$ is a holomorphic and
$\MSpace$ is a complex hyperbolic spaces in the sense of Kobayashi.
