Ivrii Conjecture for Contact Billiards

Determine whether the set of periodic contact billiard orbits has measure zero.

Background

The paper proposes contact-billiard analogues of two classical conjectures from Euclidean billiards. The first concerns the measure of the set of periodic trajectories, generalizing the role of the Ivrii conjecture to the outer contact setting.

References

(Ivrii ) Does the set of periodic contact billiard orbits have measure zero?

— Outer Contact Billiards  (2608.19393 - Caliz et al., 19 Aug 2026) in Section 6, “Open questions,” item 10(a), “Classical billiard conjectures”