Non-periodic not everywhere dense trajectories in triangular billiards

Titelangaben

Slipantschuk, Julia ; Bandtlow, Oscar F. ; Just, Wolfram:
Non-periodic not everywhere dense trajectories in triangular billiards.
In: Transactions of the American Mathematical Society. Bd. 378 (2025) . - S. 375-388.
ISSN 1088-6850
DOI: https://doi.org/10.1090/tran/9239

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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.