Event

Vadim Kaloshin, University of Maryland

Tuesday, January 22, 2019 15:00to16:00
Room 5345, Pav. André-Aisenstadt, CA

Conférence Nirenberg du CRM en analyse géométrique: Birkhoff Conjecture for convex planar billiards

Web site : http://www.crm.math.ca/Nirenberg2019/

G.D. Birkhoff introduced a mathematical billiard inside of a convex domain as the motion of a massless particle with elastic reflection at the boundary. A theorem of Poncelet says that the billiard inside an ellipse is integrable, in the sense that the neighborhood of the boundary is foliated by smooth closed curves and each billiard orbit near the boundary is tangent to one and only one such curve (in this particular case, a confocal ellipse). A famous conjecture by Birkhoff claims that ellipses are the only domains with this property. We show a local version of this conjecture – namely, that a small perturbation of an ellipse has this property only if it is itself an ellipse. This is based on several papers with A. Avila, J. De Simoi, G. Huang and A. Sorrentino.

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