Minkowski Billiards on the Hyperboloid of One Sheet

- School of Mathematics and Statistics

We give a review of Euclidean and pseudo-Euclidean billiards in the plane and in d-dimensional space. If the billiard table is bounded by confocal quadrics, periodic trajectories can be expressed in algebro-geometric terms based on work of Poncelet, Cayley, and others. In particular, we consider a billiard problem for compact domains on a hyperboloid of one sheet bounded by confocal quadrics using the pseudo-Euclidean metric. Using a matrix factorization technique of Moser and Veselov, the billiard is shown to be integrable in the sense of Liouville. Further, we derive a Cayley condition for the billiards under consideration and explore geometric consequences. This is joint work with Milena Radnovic (USYD).

 

Speaker - Sean Gasiorek is a Postdoctoral Research Associate at the University of Sydney. He received his Ph.D. from UC Santa Cruz in 2019 and moved to Sydney in August 2019.