<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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 <italic>a</italic> and every starting point x. We show that this assertion for a large class of sets does not hold for <italic>all</italic> irrational starting angles <italic>α.</italic></p></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.

Sets of Bounded Remainder for The Billiard on A Square

Uniform distribution theory

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Sets of Bounded Remainder for The Billiard on A Square"}

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...

Sets of Bounded Remainder for The Billiard on A Square

Published Online: Jan 25, 2019

Page range: 71 - 82

Received: Aug 29, 2016

Accepted: Jan 16, 2018

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

Keywords
Bounded remainder set, billiard path, discrepancy, distribution modulo 1, unfolding-technique

© 2018 Ida Aichinger et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Sets of Bounded Remainder for The Billiard on A Square

Published Online: Jan 25, 2019

Page range: 71 - 82

Received: Aug 29, 2016

Accepted: Jan 16, 2018

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

KeywordsBounded remainder set, billiard path, discrepancy, distribution modulo 1, unfolding-technique

© 2018 Ida Aichinger et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Bounded remainder set, billiard path, discrepancy, distribution modulo 1, unfolding-technique