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Disjointness of the convolutionsfor Chacon's automorphism

A. Prikhod'ko; V. Ryzhikov — 2000

Colloquium Mathematicum

The purpose of this paper is to show that if σ is the maximal spectral type of Chacon’s transformation, then for any d ≠ d’ we have $σ^{* d} ⊥ σ^{* d^{'}}$ . First, we establish the disjointness of convolutions of the maximal spectral type for the class of dynamical systems that satisfy a certain algebraic condition. Then we show that Chacon’s automorphism belongs to this class.

A new class of Ornstein transformations with singular spectrum

E. H. El Abdalaoui; F. Parreau; A. A. Prikhod'ko — 2006

Annales de l'I.H.P. Probabilités et statistiques

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