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arXiv · 2603.05998

Remarks on the outer length billiards

Misha Bialy·Serge Tabachnikov
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Abstract

We study outer length billiards; our main results are as follows. We prove 3- and 4-periodic versions of the Ivrii conjecture. We show that, for every period $n\ge 3$, there exists a functional space of billiard tables that possess invariant curves consisting of $n$-periodic points. For $n=4$, we explicitly parameterize such centrally symmetric billiard tables by functions of one variable and describe how to construct these tables geometrically, similarly to the known construction of Radon curves.

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Misha Bialy, Serge Tabachnikov. 2026-03-06. Remarks on the outer length billiards. https://arxiv.org/abs/2603.05998

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