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

2023/05/04 by Bunimovich, Leonid, Shapiro, Roberta
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2305.03095

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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