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Article Contents

# No planar billiard possesses an open set of quadrilateral trajectories

• The article is devoted to a particular case of Ivriĭ'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.
Mathematics Subject Classification: Primary: 58F22; Secondary: 34C25.

 Citation:

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