  Consider the action of an algebraic group $G$ on an irreducible algebraic
variety $X$ all defined over a field $k$. M. Rosenlicht showed that orbits in
general position in $X$ can be separated by rational invariants. We prove a
dynamical analogue of this theorem, where $G$ is replaced by a semigroup of
dominant rational self-maps of $X$. Our semigroup $G$ is not required to have
the structure of an algebraic variety and can be of arbitrary cardinality.
