# zbMATH — the first resource for mathematics

On three-periodic trajectories of multi-dimensional dual billiards. (English) Zbl 1026.37055
Summary: We consider the dual billiard map with respect to a smooth strictly convex closed hypersurface in linear $$2m$$-dimensional symplectic space and prove that it has at least $$2m$$ distinct 3-periodic orbits.

##### MSC:
 37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010) 37D50 Hyperbolic systems with singularities (billiards, etc.) (MSC2010) 70H12 Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics 58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces 37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)
Full Text: