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Self-intersection Points of Billiard Trajectories in a Square with Small Pockets
Abstract
We study the self-intersections of billiard trajectories in a square with small pockets of size ε removed from its four corners. In particular, we establish an asymptotic formula for the r-th moment of the number of self-intersection points for each positive integer r, as well as the distribution of such points.
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BibTeX
@misc{dong2026selfintersection,
title = {{Self-intersection Points of Billiard Trajectories in a Square with Small Pockets}},
author = {Anji Dong and Colin Edsey and Shuta Iwai and Alexandru Zaharescu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29659},
eprint = {2609.29659},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29659},
}
RIS
TY - UNPB
TI - Self-intersection Points of Billiard Trajectories in a Square with Small Pockets
AU - Anji Dong
AU - Colin Edsey
AU - Shuta Iwai
AU - Alexandru Zaharescu
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.29659
UR - https://arxiv.org/abs/2609.29659
AB - We study the self-intersections of billiard trajectories in a square with small pockets of size ε removed from its four corners. In particular, we establish an asymptotic formula for the r-th moment of the number of self-intersection points for each positive integer r, as well as the distribution of such points.
ER -