  We introduce the notion of a rational dynamical system extending the
classical notion of a topological dynamical system and we prove (multiple)
recurrence results for such systems via a partition theorem for the rational
numbers proved by Farmaki and the author. In particular, we extend classical
recurrence results developed by Furstenberg and Weiss. Also, we give some
applications of these topological recurrence results to topology, to
combinatorics, to diophantine approximations and to number theory.
