Return times and conjugates of an antiperiodic transformation

Abstract

AbstractDenote by G the group of all μ-preserving bijections of a Lebesgue probability space (X, Σ, μ) and by C the conjugacy class of an antiperiodic transformation σ in G. We present several new results concerning the denseness of C in G with respect to various topologies. One of these asserts that given any weakly mixing transformation τ in G and any F with μ(F) < 1, there is a transformation in C which agrees with τ a.e. on F.