Homotopical complexity of 2D billiard orbits
Homotopical complexity of 2D billiard orbits
Traditionally, rotation numbers for toroidal billiard flows are defined as the limiting vectors of average displacements per time on trajectory segments. Naturally, these creatures live in the (commutative) vector space ℝ n , if the toroidal billiard is given on the flat n -torus. The billiard trajectories, being curves, often …