Sets of bounded remainder for a continuous irrational rotation on $[0,1]^2$
Sets of bounded remainder for a continuous irrational rotation on $[0,1]^2$
We study sets of bounded remainder for the two-dimensional continuous irrational rotation $(\{x_1+t\}, \{x_2+t\alpha \})_{t \geq 0}$ in the unit square. In particular, we show that for almost all $\alpha$ and every starting point $(x_1, x_2)$, every polyg