Strictly Ergodic Models Under Face and Parallelepiped Group Actions

Abstract

The Jewett–Krieger theorem states that each ergodic system has a strictly ergodic topological model. In this article, we show that for an ergodic system one may require more properties on its strictly ergodic model. For example, the orbit closure of points in diagonal under face transforms may be also strictly ergodic. As an application, we show the pointwise convergence of ergodic averages along cubes, which was firstly proved by Assani (J Anal Math 110:241–269, 2010).

Keywords

Ergodic averages / Model / Cubes / Face transformations

Funding

NNSF(11225105)

NNSF of China(11371339)

NNSF of China(11571335)

the Fundamental Research Funds for the Central Universities