On polynomially integrable planar outer billiards and curves with symmetry property

@article{Glutsyuk2016OnPI,
title={On polynomially integrable planar outer billiards and curves with symmetry property},
author={A. A. Glutsyuk and Eugenii Shustin},
journal={Mathematische Annalen},
year={2016},
volume={372},
pages={1481-1501}
}
• Published 26 July 2016
• Mathematics
• Mathematische Annalen
We show that every polynomially integrable planar outer convex billiard is elliptic. We also prove an extension of this statement to non-convex billiards.
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The algebraic version of the Birkhoff conjecture is solved completely for billiards with a piecewise C2-smooth boundary on surfaces of constant curvature: Euclidean plane, sphere, and Lobachevsky
The famous conjecture of V.Ya.Ivrii (1978) says that {\it in every billiard with infinitely-smooth boundary in a Euclidean space the set of periodic orbits has measure zero}. In the present paper we
We consider billiard ball motion in a convex domain of a constant curvature surface influenced by the constant magnetic field. We prove that if the billiard map is totally integrable then the
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• Mathematics
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We present a solution of the algebraic version of Birkhoff Conjecture on integrable billiards. Namely we show that every polynomially integrable real bounded convex planar billiard with smooth