  Let $X$ be a proper CAT(0) space and let $G$ be a cocompact group of
isometries of $X$ which acts properly discontinuously. Charney and Sultan
constructed a quasi-isometry invariant boundary for proper CAT(0) spaces which
they called the contracting boundary. The contracting boundary imitates the
Gromov boundary for $\delta$-hyperbolic spaces. We will make this comparison
more precise by establishing some well known results for the Gromov boundary in
the case of the contracting boundary. We show that the dynamics on the
contracting boundary is very similar to that of a $\delta$-hyperbolic group. In
particular the action of $G$ on $\partial_cX$ is minimal if $G$ is not
virtually cyclic. We also establish a uniform convergence result that is
similar to the $\pi$-convergence of Papasoglu and Swenson and as a consequence
we obtain a new north-south dynamics result on the contracting boundary. We
additionally investigate the topological properties of the contracting boundary
and we find necessary and sufficient conditions for $G$ to be
$\delta$-hyperbolic. We prove that if the contracting boundary is compact,
locally compact or metrizable, then $G$ is $\delta$-hyperbolic.
