<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

Publié en ligne: 25 janv. 2019

Pages: 71 - 82

Reçu: 29 août 2016

Accepté: 16 janv. 2018

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

Mots clés
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

Publié en ligne: 25 janv. 2019

Pages: 71 - 82

Reçu: 29 août 2016

Accepté: 16 janv. 2018

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

Mots clésBounded 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.

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