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Rational Dynamical Systems

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.