|XXXIX Workshop on Geometric Methods in Physics||27.06-3.07.2021|
|IX School on Geometry and Physics||21-25.06.2021|
Billiards in ellipses revisited
Recently a Brazilian engineer, Dan Reznik, conducted numerous computer experiments involving billiards in ellipses, one of the best known completely integrable dynamical system. To the surprise of the billiard community, he has discovered a number of new properties of these billiards. For example, the sum of cosines of the angles of a periodic billiard polygon remains constant in the one-parameter family of such polygons (that exist due to the Poncelet porism). I shall present some of these results and outline their proofs. I shall also discuss some recent results related to the Poncelet porism.
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