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In his seminal paper of 1967 on disjointness in topologicaldynamics and ergodic theory H. Furstenberg started a systematicstudy of transitive dynamical systems. In recent years this workserved as a basis for a broad classification ofdynamical systems by their recurrence properties. In this paper I describe some aspects of this new theory and its connectionswith combinatorics, harmonic analysis and the theory oftopological groups.

Classifying dynamical systems by their recurrence properties