On the measure of the set of periodic points of the billiard
Let \(G\) be a bounded domain in \(\mathbb{R}^n\) \((n\geq 2)\) and let \(T\) denote the Poincaré map of the billiard flow on \(G\) defined by hitting the boundary of \(G\). It is shown that the set of \(T\)-periodic points of period 3 has Lebesgue measure zero.
scientific article; zbMATH DE number 797884