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arXiv · 1301.2904

Weak limits of powers of Chacon's automorphism

Élise Janvresse·A. A. Prikhod'Ko·Thierry De La Rue·Valery Ryzhikov
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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.

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Élise Janvresse, A. A. Prikhod'Ko, Thierry De La Rue, Valery Ryzhikov. 2013-01-14. Weak limits of powers of Chacon's automorphism. https://doi.org/10.1017/etds.2013.49

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