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Статья

No planar billiard possesses an open set of quadrilateral trajectories

Journal of Modern Dynamics. 2012. Vol. 6. No. 3. P. 287-326.
Glutsyuk A., Kudryashov Y.

The article is devoted to a particular case of Ivrǐ's conjecture on periodic orbits of billiards. The general conjecture states that the set of periodic orbits of the billiard in a domain with smooth boundary in the Euclidean space has measure zero. In this article we prove that for any domain with piecewise C 4-smooth boundary in the plane the set of quadrilateral trajectories of the corresponding billiard has measure zero.