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, D. Sorrentino.
Samstag, den 28. Oktober 2017 um 10.00-11.00 Uhr, in Mathematikon, INF 205, Konferenzraum, 5. OG Samstag, den 28. Oktober 2017 at 10.00-11.00, in Mathematikon, INF 205, Konferenzraum, 5. OG
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. P. Albers