A curious dynamical system in the plane

Stefan Steinerberger, Tony Zeng

For any irrational $\alpha >0$ and any initial value $z_{-1}\in \mathbb{C}$, we define a sequence of complex numbers $(z_n{)}_{n=0}^{\infty }$ as follows: $z_n$ is $z_{n-1}+e^{2\pi i\alpha n}$…