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arXiv · 2406.17734

Non-periodic not everywhere dense trajectories in triangular billiards

Julia Slipantschuk·Oscar F. Bandtlow·Wolfram Just
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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.

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Julia Slipantschuk, Oscar F. Bandtlow, Wolfram Just. 2024-06-25. Non-periodic not everywhere dense trajectories in triangular billiards. https://doi.org/10.1090/tran%2F9239

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