# gst: foliated by invariant quadrics, outer contact billiards.

<< ️(AA) introduce outer contact billiards as an odd dimensional counterpart to outer symplectic billiards. Until now, outer billiards have only been considered in even dimensional symplectic vector spaces. By projectivizing outer symplectic billiards, (They) obtain outer contact billiards, where the affine midpoint condition descends to its projective analog, namely harmonic conjugation. (They) prove that outer contact billiards generate contactomorphisms. >>

<< ️For quadratic surfaces in RP^3, (AA) show that the correspondence is completely integrable: its domain is foliated by invariant quadrics and, on each leaf, the dynamics is determined by the iteration of an explicit linear transformation. (They) also establish two rigidity results for periodic trajectories: outer contact billiards admit no 3-periodic orbits and, among quadratic tables, only one admits 4-periodic orbits. >>

Ana Chavez Caliz, Connor Jackman. Outer Contact Billiards. arXiv: 2608.19393v1 [math.DS]. Aug 19, 2026.

https://arxiv.org/abs/2608.19393

Also: billiard, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, billiard, outer contact billiards, symplectic billiards, harmonic conjugation, contactomorphisms, foliated domain.