A characterization of weak-mixing for minimal systems

Abstract

Let (X,T) be a non-trivial minimal topological dynamical system. We proved that (X,T) is weak-mixing if and only if there exists a dense σ-Cantor subset K of X such that for each d∈N, Kd is contained in the set of transitive points of the map T×T2×⋯×Td. We also give the polynomial extension of the result.