Integrability of Higher-Dimensional Quadratic Tables

Determine whether outer contact billiards over quadratic hypersurfaces remain integrable in projective contact spaces of dimensions higher than three.

Background

In projective three-space, the paper proves complete integrability for quadratic tables and describes the dynamics on invariant quadrics by fixed linear transformations. The appendix explains that higher-dimensional quadratic tables can have additional integrals and branched dynamics, so the persistence of integrability is unresolved.