Dynamics of Higher-Degree Tables

Characterize the dynamics of outer contact billiards over tables of degree greater than two, including the resulting branched dynamics and associated focal surfaces.

Background

The paper gives a complete description for quadratic tables in projective three-space. For higher-degree algebraic tables, a point can lie on many characteristic lines, producing branched rather than ordinary two-valued dynamics; the structure of these systems is not determined.

References

What can one say about higher degree tables?

— Outer Contact Billiards  (2608.19393 - Caliz et al., 19 Aug 2026) in Section 6, “Open questions,” item 6

What sort of behaviors can appear around these singular points? When is it possible to regularize the correspondence through such singularities?

— Outer Contact Billiards  (2608.19393 - Caliz et al., 19 Aug 2026) in Section 6, “Open questions,” item 8