On two classes of dense 2-generator subgroups in $\mathbb C$
  We consider dense 2-generator multiplicative subgroups in $\mathbb C$ and show that for each point $z\in \mathbb C$ the set of limit values for the arguments of the powers of each generator at the point $z$ is either finite or is $[-\pi,\pi]$ 
Kirill Kamalutdinov and Andrey Tetenov and Dmitry Vaulin
math.DS math.GT