On quadrilateral orbits in planar billiards
The authors state several results in the direction of Ivrii's conjecture which asserts that the set of periodic billiard orbits in a domain \(\Omega\subset {\mathbb R}^m\) has measure zero in the space of all billiard trajectories, assuming that the boundary \(\partial \Omega\) is sufficiently smooth. One of the main results of the paper states that for any planar billiard domain with piecewise analytic boundary the set \(\text{Per}_4\) has no interior points.
scientific article; zbMATH DE number 5998413
scientific article