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 facting 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.