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 corresponding ones enjoyed by the classical Anzai skew-product. As an application, for a uniquely ergodic Anzai skew-product on the non-commutative -torus , , we investigate the pointwise limit, , for and a point in the unit circle, and show that there are examples for which the limit does not exist, even in the weak topology.
DEL VECCHIO, S., Fidaleo, F., Giorgetti, L., Rossi, S. (2020). Ergodic properties of the Anzai skew-product for the noncommutative torus. ERGODIC THEORY & DYNAMICAL SYSTEMS, 41(4), 1064-1085 [10.1017/etds.2019.116].
Ergodic properties of the Anzai skew-product for the noncommutative torus
del vecchio simone
;fidaleo francesco
;giorgetti luca
;
2020-11-01
Abstract
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 corresponding ones enjoyed by the classical Anzai skew-product. As an application, for a uniquely ergodic Anzai skew-product on the non-commutative -torus , , we investigate the pointwise limit, , for and a point in the unit circle, and show that there are examples for which the limit does not exist, even in the weak topology.File | Dimensione | Formato | |
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