We consider the dual billiard map with respect to a smooth strictly convex closed hypersurface in linear –dimensional symplectic space and prove that it has at least distinct 3–periodic orbits.
"On three-periodic trajectories of multi-dimensional dual billiards." Algebr. Geom. Topol. 3 (2) 993 - 1004, 2003. https://doi.org/10.2140/agt.2003.3.993