of accumulation points in $\partial
\tilde M$ of a fixed orbit $\Gamma x$ $(x\in \tilde M)$ of the action of $\Gamma$ on $\tilde M$. We always assume that the group $\Gamma$ is non-elementary, i.e. that its limit set contains as least 3 points. Then $\Lambda$ is the smallest nontrivial closed subset of $\partial\tilde M$ which is invariant under the action of $\Gamma$.

The *geodesic flow* $\Phi^t$ acts on the *unit tangent bundle* $T^1\tilde M$ of $\tilde M$ and on the unit tangent bundle $T^1M$ of $M$. Let $\tilde L\subset T^1\tilde M$ be the set of all unit tangents of all geodesics with both end-points in $\Lambda$. Then $\tilde L$ is invariant under the action of $\Phi^t$ and the action of $\Gamma$. The quotient $L=\tilde L/\Gamma$ is just the *non-wandering set* for the action of $\Phi^t$ on $T^1 M$. Since $M$ is convex cocompact by assumption, $L$ is a compact hyperbolic set for the geodesic flow $\Phi^t$ on $T^1M$. The sets $\tilde L$ and $L$ are moreover invariant under the *flip* ${{\mathcal{F}}}:v\to -v$ which maps a unit tangent vector to its negative. The Riemannian metric on $M$ induces a complete Riemannian metric and hence a complete distance function $d$ on $T^1M$.

