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SUMMARY:Misha Bialy (Tel Aviv University)
DTSTART:20201118T121000Z
DTEND:20201118T133000Z
DTSTAMP:20260423T005710Z
UID:GDS/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GDS/15/">The
  Birkhoff-Poritsky conjecture for centrally-symmetric billiard tables</a>\
 nby Misha Bialy (Tel Aviv University) as part of Geometry and Dynamics sem
 inar\n\n\nAbstract\nIn this talk (joint work with A.E. Mironov) I shall di
 scuss a recent \nproof of the Birkhoff-Poritsky conjecture for centrally-s
 ymmetric \nC^2-smooth convex planar billiards. We assume that the domain  
 between \nthe invariant curve of 4-periodic orbits and the boundary of the
  phase \ncylinder is foliated by C^0-invariant curves. Under this assumpti
 on we \nprove that the billiard curve is an ellipse. The main ingredients 
 of \nthe proof are : (1) the non-standard generating function for convex \
 nbilliards\; (2) the remarkable structure of the invariant curve \nconsist
 ing of 4-periodic orbits\; and (3) the integral-geometry \napproach initia
 ted for rigidity results of circular billiards. \nSurprisingly\, our resul
 t yields a Hopf-type rigidity for billiard \nin ellipse.\n
LOCATION:https://researchseminars.org/talk/GDS/15/
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