Non-periodic not everywhere dense trajectories in triangular billiards
arXiv:2406.17734 · doi:10.1090/tran/9239
Abstract
Building on tools that have been successfully used in the study of rational billiards, such as induced maps and interval exchange transformations, we provide a construction of a one-parameter family of isosceles triangles exhibiting non-periodic trajectories that are not everywhere dense. This provides, by elementary means, a definitive negative answer to a long-standing open question on the density of non-periodic trajectories in triangular billiards.
15 pages, 2 figures