Examples of projective billiards with open sets of periodic orbits - Fiorebe, Corentin (Discrete and Continuous Dynamical Systems- Series A, 2024)
In the class of projective billiards, which contains the usual billiards, we exhibit counter-examples to Ivrii's conjecture, which states that in any planar billiard with smooth boundary the set of periodic orbits has zero measure. The counter-examples are polygons admitting a 2-parameters family of n-periodic orbits, with n being either 3 or any even integer greater than 4.
epub_ahead
yes
Keywords: article