On projective billiards with open sets of periodic orbits

A billiard is a bounded domain in which we study the trajectory of a ray of light obtained after successive reflections on the boundary of the domain viewed as a perfectly reflecting mirror. Reflections are given by the classical law of optics: angle of incidence = angle of reflection. These dynamical systems are intensively studied, and many interesting questions arise. Ivriis conjecture is one of them: it states that given a billiard in a Euclidean space, the set of its periodic orbits has zero measure. During this talk, we will present another type of billiards introduced by S. Tabachnikov called projective billiards, which generalizes different types of billiards, and show how they can be useful to understand questions related to usual billiards like Ivriis conjecture.