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Journal

Uniform Distribution Theory (UDT)


Volume & Issue

UDT. Volume 13. Issue 2


Published on

December, 2018


Pages

71-82


DOI

https://doi.org/10.2478/udt-2018-0011

Article

Sets of Bounded Remainder for The Billiard on A Square


Authors

Ida Aichinger and Gerhard Larcher


Abstract

We study sets of bounded remainder for the billiard on the unit square. In particular, we note that every convex set S whose boundary is twice continuously differentiable with positive curvature at every point, is a bounded remainder set for almost all starting angles a and every starting point x. We show that this assertion for a large class of sets does not hold for all irrational starting angles α.


Citation

Aichinger, I. & Larcher, G. (2018). Sets of Bounded Remainder for The Billiard on A Square. Uniform distribution theory, 13(2), 71-82. https://doi.org/10.2478/udt-2018-0011