Classifying dynamical systems by their recurrence properties

Abstract

In his seminal paper of 1967 on disjointness in topological
dynamics and ergodic theory H. Furstenberg started a systematic
study of transitive dynamical systems. In recent years this work
served as a basis for a broad classification of
dynamical systems by their recurrence properties. In this paper
I describe some aspects of this new theory and its connections
with combinatorics, harmonic analysis and the theory of
topological groups.