# Anzai flow in noncommutative geometry

Consider Anzai flows (cf. Anzai: Ergodic Skew Product Transformations on the Torus, Osaka Math. J. 3 (1951), 83-99) on the two dimensional torus $$T^2$$. I would like to know if there exists some generalization of the related automorphisms on $$C(T^2)$$ (the commutative $$C^*$$-algebras made of all continuous functions on $$T^2$$) of such homeomorphisms, to the noncommutative 2-torus $$A_\theta$$.