Collisions in semi-dispersing billiard on Riemannian manifold (Q1612238)

The authors prove first for semidispersing billiards on arbitrary manifolds any trajectory makes only a finite number of collisions during a finite period of time. Then they establish local uniform estimates on the number of collisions for such billiards under a mild nondegeneracy condition. Moreover, the authors give effective estimates on the maximal number of collisions and the size of the neighborhood in which they may occur in terms of the nondegeneracy constant and some geometric properties of the manifold.