On Conjugacy of Convex Billiards
| Symplectic Dynamics Seminar | |
| Topic: | On Conjugacy of Convex Billiards |
| Speaker: | Vadim Kaloshin |
| Affiliation: | Pennsylvania State University; Member, School of Mathematics |
| Date: | Wednesday, January 25 |
| Time/Room: | 2:00pm - 3:00pm/S-101 |
There are indications that in the 80s Guillemin posed a question: If billiard maps are conjugate, can we say that domains are the same up to isometry?
On one side, we show that conjugacy of different domains can't be C^1 near the boundary. In particular, billiard maps of the circle and an ellipse are both analytically integrable, but not C^1 conjugate. On the other side, if conjugate near the boundary s smoother, then domains are the same up to isometry.
(This is joint work with A. Sorrentino.)