Polygonal Refractive Outer Billiards

Jaewoo Park

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arXiv · 2608.02936

Polygonal Refractive Outer Billiards

Jaewoo Park

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Abstract

Extending recent work on refractive billiards, we introduce and study the corresponding refractive outer billiards system about a convex polygon. Gutkin and Simanyi showed in 1992 that for regular outer billiards, orbits about a certain class of polygons called quasi-rational polygons are bounded, and that orbits about rational polygons are periodic. Tabachnikov and Culter later proved in 2007 that every outer billiard system about a convex polygon admits a periodic trajectory. We generalize both results to the refractive setting.

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Jaewoo Park. 2026-08-03. Polygonal Refractive Outer Billiards. https://arxiv.org/abs/2608.02936

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