Consider Anzai flows (cf. Anzai: Ergodίc 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 automorphisms of the noncommutative 2-torus $C^*$-algebra $A_\theta$.


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