English

Long and Short Periodic Billiard Trajectories in the Regular Pentagon

Dynamical Systems 2021-11-19 v1

Abstract

In any periodic direction on the regular pentagon billiard table, there exists two combinatorially different billiard paths, with one longer than the other. For each periodic direction, McMullen asked if one could determine whether the periodic trajectory through a given point is long, short, or a saddle connection. In this paper we present an algorithm resolving this question for trajectories emanating from the midpoints of the pentagon.

Keywords

Cite

@article{arxiv.2111.09856,
  title  = {Long and Short Periodic Billiard Trajectories in the Regular Pentagon},
  author = {Samuel Everett and Vanessa Lin and Aidan Mager},
  journal= {arXiv preprint arXiv:2111.09856},
  year   = {2021}
}

Comments

11 pages, 12 figures