Ergodic properties of the Anzai skew-product for the non-commutative torus

• Published in: Ergodic theory and dynamical systems Vol. 41; no. 4; pp. 1064 - 1085
• Main Authors: DEL VECCHIO, SIMONE, FIDALEO, FRANCESCO, GIORGETTI, LUCA, ROSSI, STEFANO
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 01.04.2021
• Subjects: Cartesian coordinates; Ergodic processes; Original Article; Topology; Toruses; non-commutative torus; skew-product; 37A55; 58B34; 58J51; operator algebras; ergodic dynamical systems; unique ergodicity; 46L55; 46L65

We provide a systematic study of a non-commutative extension of the classical Anzai skew-product for the cartesian product of two copies of the unit circle to the non-commutative 2-tori. In particular, some relevant ergodic properties are proved for these quantum dynamical systems, extending the cor...