Non-periodic not everywhere dense trajectories in triangular billiards
Dynamical Systems
2024-06-26 v1
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.
Keywords
Cite
@article{arxiv.2406.17734,
title = {Non-periodic not everywhere dense trajectories in triangular billiards},
author = {Julia Slipantschuk and Oscar F. Bandtlow and Wolfram Just},
journal= {arXiv preprint arXiv:2406.17734},
year = {2024}
}
Comments
15 pages, 2 figures