At the 2019 Sydney workshop on mathematical billiards, Sonia Pinto-de-Carvalho proposed the question whether there is a surface where the geodesic circular billiard is not integrable. In other words, consider a 2-dimensional Riemannian manifold M and a domain D in M such that the boundary of D is a circle. Now consider a point particle which moves in D with unit velocity along geodesics until it hits the boundary, where it gets reflected elastically. The resulting dynamical system - the circular billiard - is clearly fully integrable when M is the Euclidean plane or a sphere. But can it also be non-integrable?
In this talk I present a positive answer by constructing many examples of non-integrable circular billiards, and ask some further questions about even more possible examples.
This is joint work with Alexey Glutsyuk.
Non-integrability in circular billiards
13.03.2020 15:30 - 16:30
Organiser:
H. Bruin, R. Zweimüller
Location: