  We introduce new techniques for studying boundary dynamics of CAT(0) groups.
For a group $G$ acting geometrically on a CAT(0) space $X$ we show there is a
flat $F\subset X$ of maximal dimension whose boundary sphere intersects every
minimal $G$-invariant subset of $\partial_\infty X$. As a result we derive a
necessary and sufficient dynamical condition for $G$ to be virtually-Abelian,
as well as a new approach to Ballmann's rank rigidity conjecture.
