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Sets of Bounded Remainder for the Continuous Irrational Rotation on $ by Grepstad, Sigrid; Larcher, Gerhard is a scholarly article available to read on EtoBox.

What is Sets of Bounded Remainder for the Continuous Irrational Rotation on $ about?

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 polygon $S$ with no edge of slope $\alpha$ is a set of bounded remainder. Moreover, every convex set $S$ whose boundary is twice continuously differentiable with positive curvature at every point is a bounded remainder set for almost all $\alpha$ and every starting point $(x_1, x_2)$. Finally we show that these assertions are, in some sense, best possible.

Author

Grepstad, Sigrid; Larcher, Gerhard

Published

2016

Language

EN