Convergence of multiple ergodic averages along cubes for several commuting transformations

Qing Chu (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We prove the norm convergence of multiple ergodic averages along cubes for several commuting transformations, and derive corresponding combinatorial results. The method we use relies primarily on the ``magic extension" established recently by B. ~Host.

Mots clés: Averages along cubes; commuting transformations; magic system; ergodic seminorms

Domaines: Systèmes dynamiques [math.DS]

Qing Chu. Convergence of multiple ergodic averages along cubes for several commuting transformations. 2008. ⟨hal-00341285v2⟩