This talk is motivated by the study of geometric routing algorithms used for navigating stationary point processes. The mathematical abstraction for such a navigation is a class of non-measure preserving dynamical systems on counting measures called point-maps. The talk will focus on two objects associated with a point map $f$ acting on a stationary point process $Phi$: * The $f$-probabilities of $Phi$, which can be interpreted as the stationary regimes of the routing algorithm $f$ on $Phi$. These probabilities are defined from the compactification of the action of the semigroup of point-map translations on the space of Palm probabilities. The $f$-probabilities of $Phi$ are not always Palm distributions. * The $f$-foliation of $Phi$, a partition of the support of $Phi$ which is the discrete analogue of the stable manifold of $f$, i.e., the leaves of the foliation are the points of $Phi$ with the same asymptotic fate for $f$. These leaves are not always stationary point processes. There always exists a point-map allowing one to navigate the leaves in a measure-preserving way. Joint work with Mir-Omid Haji-Mirsadeghi, Sharif University, Department of Mathematics.