Article
Sets of Bounded Remainder for the Billiard on a Square
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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 a.
Keywords
Bounded remainder set, billiard path, discrepancy, distribution modulo 1.
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
I. Aichinger and G. Larcher, “Sets of bounded remainder for the billiard on a square,” Uniform Distribution Theory, vol. 13, no. 2, pp. 71–82, 2018, doi: 10.2478/udt-2018-0011.
Aichinger I, Larcher G. Sets of bounded remainder for the billiard on a square. Uniform Distribution Theory. 2018;13(2):71–82. doi:10.2478/udt-2018-0011.
Aichinger, I. and Larcher, G. (2018), ‘Sets of bounded remainder for the billiard on a square’, Uniform Distribution Theory, 13(2), pp. 71–82. Available at: https://doi.org/10.2478/udt-2018-0011.
Aichinger, Ida, and Gerhard Larcher. “Sets of Bounded Remainder for the Billiard on a Square.” Uniform Distribution Theory, vol. 13, no. 2, 2018, pp. 71–82. https://doi.org/10.2478/udt-2018-0011.
Aichinger, Ida, and Gerhard Larcher. “Sets of Bounded Remainder for the Billiard on a Square.” Uniform Distribution Theory 13, no. 2 (2018): 71–82. https://doi.org/10.2478/udt-2018-0011.
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Published by: Engineering Journals
