Uniform rigidity sequences for weak mixing diffeomorphisms on ${\mathbb{T}}^2$

Abstract

In this paper we will show that if a sequence of natural numbers satisfies a certain growth rate, then there is a weak mixing diffeomorphism on ${\mathbb{T}}^2$ that is uniformly rigid with respect to that sequence. The proof is based on a quantitative version of the Anosov-Katok-method with explicitly defined conjugation maps and the constructions are done in the $C^{\infty }$-topology as well as in the real-analytic topology.