Hamiltonian Systems

The usual outer billiard can be defined in variational terms, with area as generating function. One can define an analogous outer length billiard. Recent work has begun to explore this system, which turns out to be a twist map preserving a certain symplectic form. In this talk, I will present results regarding the behavior of orbits "at infinity" as well as a surprising and non-trivial connection between the usual outer billiard and the outer length billiard. I will also discuss conjectures and experimental results in the polygonal case. This work is partly joint with P. Albers and S. Tabachnikov.