For billiards with N obstacles on a torus, we study the behavior of specific kind of its trajectories, the so called admissible trajectories. Using the methods developed in Blokh et al. (Commun Math Phys 266:239–265, 2006), we prove that the admissible rotation set is convex, and the periodic trajectories of admissible type are dense in the admissible rotation set. In addition, we show that the admissible rotation set is a proper subset of the general rotation set.
Torus General rotation set Admissible rotation set Rotation vector
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