Ergodic seminorms for commuting transformations and applications

Bernard Host (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

Recently, T. Tao gave a finitary proof a convergence theorem for multiple averages with several commuting transformations and soon later, T.~Austin gave an ergodic proof of the same result. Although we give here one more proof of the same theorem, this is not the main goal of this paper. Our main concern is to provide some tools for the case of several commuting transformations, similar to the tools successfully used in the case of a single transformation, with the idea that they will be useful in the solution of other problems.

Mots clés: multiple ergodic averages; commuting transformations; ergodic seminorms

Domaines: Systèmes dynamiques [math.DS]

Bernard Host. Ergodic seminorms for commuting transformations and applications. Studia Mathematica, 2009, 195, pp.31-49. ⟨hal-00340769⟩