Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - Université de Rouen Normandie

A general question in ergodic theory or topological dynamical systems is for which subset S of Z there is a point whose orbit along S is dense in the whole space, or the time averages of a function along S converge to its integral. In this talk, I will explain how one can show that for a totally minimal system and S being the values of a given integer polynomial on Z, such x exists. This result was developed gradually in the works by Huang-Shao-Ye, Glasner-Huang-Shao-Weiss-Ye, and Qiu.