Periods of Clifford-Torus Dynamics

Determine which periods can occur for a fixed Clifford torus under the outer contact billiard correspondence.

Background

The dynamics on each Clifford torus is determined by two rotation frequencies satisfying an explicit Kepler-type relation. Although the paper identifies parameter values for which periodic orbits occur, it does not classify all periods for a fixed Clifford torus.

References

For a given Clifford torus, which periods can actually occur?

— Outer Contact Billiards  (2608.19393 - Caliz et al., 19 Aug 2026) in Section 6, “Open questions,” item 11, “Periodic Clifford tori”