Symplectic Geometry Seminar

By the Birkhoff Ergodic Theorem, the asymptotic mean action of an area-preserving map is defined almost everywhere. Bramham and Zhang asked whether, if a map is a pseudo-rotation, its asymptotic mean action is defined everywhere and is constant. In this talk, I will explain how to show that the asymptotic mean action and the asymptotic linking number of pseudo-rotations are defined everywhere and are constant for every $C^{1}$  pseudo-rotation that is conjugate to a rotation on the boundary.  This is joint work with David Bechara and Patrice Le Calvez.