Hofer’s metric dH is a remarkable bi-invariant metric on the group of Hamiltonian diffeomorphisms of a symplectic manifold. In my talk, I will explain a result, obtained jointly with Matthias Meiwes, which says that the braid type of a set of periodic orbits of a Hamiltonian diffeomorphism on a closed surface is stable under perturbations that are sufficiently small with respect to Hofer’s metric. As a consequence of this we obtained that the topological entropy, seen as a function on the space of Hamiltonian diffeomorphisms of a closed surface, is lower semi-continuous with respect to the Hofer metric dH.
If time permits, I will explain related questions for Reeb flows on 3-manifolds and Hamiltonian diffeomorphisms on higher-dimensional symplectic manifolds, and recent progress on these problems obtained by myself, Meiwes, Abror Pirnapasov and Lucas Dahinden.
This video is part of the Institute for Advanced Study‘s Symplectic geometry seminar.
