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arXiv · 2305.03095

A challenger to elliptic billiards fails: String construction over convex polygons and the Birkhoff--Poritsky conjecture

Leonid Bunimovich·Roberta Shapiro
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Abstract

We prove that the billiard claimed to be a possible counterexample to the Birkhoff-Poritsky conjecture is actually not a counterexample. We also show that for a billiard in a table obtained by the string construction over any convex polygon, this polygon is a core of the billiard dynamics.

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Leonid Bunimovich, Roberta Shapiro. 2023-05-04. A challenger to elliptic billiards fails: String construction over convex polygons and the Birkhoff--Poritsky conjecture. https://arxiv.org/abs/2305.03095

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