Weak limits of powers of Chacon's automorphism

Abstract

We completely describe the weak closure of the powers of the Koopman operator associated to Chacon's classical automorphism. We show that weak limits of these powers are the ortho-projector to constants and an explicit family of polynomials. As a consequence, we answer negatively the question of alpha-weak mixing for Chacon's automorphism.

References in corpus (3)

• On spectral disjointness of powers for rank-one transformations and Möbius orthogonality
• Minimal Self-Joinings, Bounded Constructions, and Weak Closure of Ergodic Actions
• Several questions and hypotheses concerning the limit polynomials for Chacon transformation