Weak limits of powers of Chacon's automorphism
Dynamical Systems
2019-02-20 v1
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.
Cite
@article{arxiv.1301.2904,
title = {Weak limits of powers of Chacon's automorphism},
author = {Élise Janvresse and A. A. Prikhod'Ko and Thierry De La Rue and Valery Ryzhikov},
journal= {arXiv preprint arXiv:1301.2904},
year = {2019}
}