对椭圆台球的一个反例挑战失败：凸多边形上的弦构造与 Birkhoff–Poritsky 猜想
动力系统
2024-04-04 v2
摘要
我们证明，被声称可能是 Birkhoff–Poritsky 猜想反例的台球实际上并非反例。我们还证明，对于由任意凸多边形上的弦构造所得台球桌中的台球，该多边形是台球动力学的核。
引用
@article{arxiv.2305.03095,
title = {A challenger to elliptic billiards fails: String construction over convex polygons and the Birkhoff--Poritsky conjecture},
author = {Leonid Bunimovich and Roberta Shapiro},
journal= {arXiv preprint arXiv:2305.03095},
year = {2024}
}
备注
Proof error: Elliptic arcs that create billiard table may have caustics that correspond to open billiard systems (and therefore are not also elliptic arcs)