Convergence of Conze-Lesigne averages

Bernard Host (1) , B Kra

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We study the convergence of N-1 Sigmaf(1)(T(a1n)x)f(2)(T(a2n)x)f(3)(T(a3n)x), for a measure-preserving system (X, B, mu, T) and f(1), f(2), f(3) is an element of L(infinity)(mu). This generalizes the theorem of Conze and Lesigne on such expressions and simplifies the proof. We also obtain a description of the limit.

Domaines: Physique mathématique [math-ph]

Bernard Host, B Kra. Convergence of Conze-Lesigne averages. Ergodic Theory and Dynamical Systems, 2001, 21 (?), pp.493--509. ⟨hal-00693738⟩