Appears in collection : Probabilities days / Journées de probabilités

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. Chacon's automorphism - Koopman operator - weak limit - alpha-weak mixing