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VIDEO LIBRARY |
Dynamics in Siberia - 2019
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Plenary talks
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On polynomially integrable billiards on surfaces of constant curvature A. A. Glutsyuk |
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Abstract: The famous Birkhoff Conjecture deals with convex bounded planar billiard The polynomial version of the Birkhoff Conjecture, which was first stated and studied by Sergey Bolotin in 1990, concerns polynomially integrable billiards, where there exists a first integral polynomial in the velocity that is non-constant on the unit level hypersurface of the module of the velocity. In this talk we present a brief survey of Birkhoff Conjecture and a complete solution of its polynomial version. We prove that each bounded polynomially integrable planar billiard with References [1] Bialy, M.; Mironov, A.E. Angular billiard and algebraic Birkhoff conjecture. Adv. in Math. 313 (2017), 102–126. [2] Bialy, M.; Mironov, A.E. Algebraic Birkhoff conjecture for billiards on Sphere and Hyperbolic plane. J. Geom. Phys., 115 (2017), 150–156. [3] Glutsyuk, A. On polynomially integrable Birkhoff billiards on surfaces of constant curvature. - To appear in J. Eur. Math. Soc. Available at https://arxiv.org/abs/1706.04030 [4] Glutsyuk, A. On two-dimensional polynomially integrable Birkhoff billiards on surfaces of constant curvature. Doklady Mathematics, 98 (2018), No.1, 382–385. [5] Kaloshin, V.; Sorrentino, A. On local Birkhoff Conjecture for convex billiards. Ann. of Math., 188 (2018), No. 1, 315–380. Language: English |