Non-periodic not everywhere dense trajectories in triangular billiards

Slipantschuk, Julia; Bandtlow, Oscar F.; Just, Wolfram

doi:10.1090/tran/9239

Non-periodic not everywhere dense trajectories in triangular billiards
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by Julia Slipantschuk, Oscar F. Bandtlow and Wolfram Just;

Trans. Amer. Math. Soc. 378 (2025), 375-388

DOI: https://doi.org/10.1090/tran/9239

Published electronically: October 25, 2024

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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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Non-periodic not everywhere dense trajectories in triangular billiards
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Abstract: