A new class of Ornstein transformations with singular spectrum

El Houcein El Abdalaoui (1) , François Parreau (2) , A. A. Prikhod'Ko (3)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem
2 LAGA - Laboratoire Analyse, Géométrie et Applications
3 Faculty of Mathematics and Computer Science and Institute of Mathematics

It is shown that for any family of probability measures in Ornstein type constructions the corresponding transformation has almost surely a singular spectrum. This is a new generalization of Bourgain's theorem , the same result is proved for Rudolph's construction.

Mots clés: Ornstein transformations; simple Lebesgue spectrum; singular spectrum; generalized Riesz products; rank one transformations

Domaines: Systèmes dynamiques [math.DS]

El Houcein El Abdalaoui, François Parreau, A. A. Prikhod'Ko. A new class of Ornstein transformations with singular spectrum. 2005. ⟨hal-00004247⟩