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arXiv · 2002.09845

Examples of reflective projective billiards and outer ghost billiards

Corentin Fierobe
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Abstract

In the class of projective billiards, which contains the usual billiards, we exhibit counter-examples to Ivrii's conjecture, which states that in any planar billiard with smooth boundary the set of periodic orbits has zero measure. The counter-examples are polygons admitting a $2$-parameters family of $n$-periodic orbits, with $n$ being either $3$ or any even number grower than $4$.

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Corentin Fierobe. 2020-02-23. Examples of reflective projective billiards and outer ghost billiards. https://arxiv.org/abs/2002.09845

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